LMFDB - Embedded newform 315.2.k.b.16.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(16,315)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("315.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.k (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			16.6
Character	$\chi$	$=$	315.16
Dual form			315.2.k.b.256.6

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.148731 - 0.257610i) q^{2} +(0.310785 - 1.70394i) q^{3} +(0.955758 - 1.65542i) q^{4} -1.00000 q^{5} +(-0.485175 + 0.173367i) q^{6} +(-2.64436 + 0.0857253i) q^{7} -1.16353 q^{8} +(-2.80683 - 1.05912i) q^{9} +O(q^{10})$	\(q+(-0.148731 - 0.257610i) q^{2} +(0.310785 - 1.70394i) q^{3} +(0.955758 - 1.65542i) q^{4} -1.00000 q^{5} +(-0.485175 + 0.173367i) q^{6} +(-2.64436 + 0.0857253i) q^{7} -1.16353 q^{8} +(-2.80683 - 1.05912i) q^{9} +(0.148731 + 0.257610i) q^{10} +4.84852 q^{11} +(-2.52370 - 2.14304i) q^{12} +(-2.59263 - 4.49056i) q^{13} +(0.415382 + 0.668463i) q^{14} +(-0.310785 + 1.70394i) q^{15} +(-1.73846 - 3.01111i) q^{16} +(1.80070 + 3.11891i) q^{17} +(0.144623 + 0.880589i) q^{18} +(-2.03033 + 3.51663i) q^{19} +(-0.955758 + 1.65542i) q^{20} +(-0.675758 + 4.53248i) q^{21} +(-0.721125 - 1.24902i) q^{22} +0.983576 q^{23} +(-0.361607 + 1.98258i) q^{24} +1.00000 q^{25} +(-0.771208 + 1.33577i) q^{26} +(-2.67699 + 4.45350i) q^{27} +(-2.38546 + 4.45947i) q^{28} +(2.30352 - 3.98981i) q^{29} +(0.485175 - 0.173367i) q^{30} +(3.60041 - 6.23609i) q^{31} +(-1.68065 + 2.91098i) q^{32} +(1.50685 - 8.26159i) q^{33} +(0.535640 - 0.927756i) q^{34} +(2.64436 - 0.0857253i) q^{35} +(-4.43593 + 3.63422i) q^{36} +(3.25248 - 5.63347i) q^{37} +1.20789 q^{38} +(-8.45740 + 3.02208i) q^{39} +1.16353 q^{40} +(-0.298439 - 0.516911i) q^{41} +(1.26812 - 0.500038i) q^{42} +(0.0565258 - 0.0979056i) q^{43} +(4.63401 - 8.02634i) q^{44} +(2.80683 + 1.05912i) q^{45} +(-0.146288 - 0.253378i) q^{46} +(-3.57890 - 6.19883i) q^{47} +(-5.67104 + 2.02643i) q^{48} +(6.98530 - 0.453377i) q^{49} +(-0.148731 - 0.257610i) q^{50} +(5.87406 - 2.09898i) q^{51} -9.91170 q^{52} +(4.78827 + 8.29352i) q^{53} +(1.54542 + 0.0272455i) q^{54} -4.84852 q^{55} +(3.07679 - 0.0997437i) q^{56} +(5.36113 + 4.55247i) q^{57} -1.37042 q^{58} +(3.75057 - 6.49618i) q^{59} +(2.52370 + 2.14304i) q^{60} +(7.49581 + 12.9831i) q^{61} -2.14197 q^{62} +(7.51306 + 2.56008i) q^{63} -5.95400 q^{64} +(2.59263 + 4.49056i) q^{65} +(-2.35238 + 0.840575i) q^{66} +(3.78548 - 6.55664i) q^{67} +6.88414 q^{68} +(0.305681 - 1.67595i) q^{69} +(-0.415382 - 0.668463i) q^{70} +10.2073 q^{71} +(3.26582 + 1.23231i) q^{72} +(-1.67879 - 2.90775i) q^{73} -1.93498 q^{74} +(0.310785 - 1.70394i) q^{75} +(3.88100 + 6.72209i) q^{76} +(-12.8212 + 0.415641i) q^{77} +(2.03639 + 1.72923i) q^{78} +(-2.59268 - 4.49066i) q^{79} +(1.73846 + 3.01111i) q^{80} +(6.75654 + 5.94552i) q^{81} +(-0.0887742 + 0.153761i) q^{82} +(-5.45891 + 9.45512i) q^{83} +(6.85730 + 5.45062i) q^{84} +(-1.80070 - 3.11891i) q^{85} -0.0336285 q^{86} +(-6.08250 - 5.16504i) q^{87} -5.64138 q^{88} +(-7.64065 + 13.2340i) q^{89} +(-0.144623 - 0.880589i) q^{90} +(7.24080 + 11.6524i) q^{91} +(0.940061 - 1.62823i) q^{92} +(-9.50697 - 8.07296i) q^{93} +(-1.06458 + 1.84392i) q^{94} +(2.03033 - 3.51663i) q^{95} +(4.43781 + 3.76842i) q^{96} +(6.85013 - 11.8648i) q^{97} +(-1.15572 - 1.73205i) q^{98} +(-13.6089 - 5.13516i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) $ 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.148731	−	0.257610i	−0.105169	−	0.182157i	0.808638	−	0.588306i	$-0.200205\pi$
$2$	−0.148731	−	0.257610i	−0.105169	−	0.182157i	−0.913807	+	0.406148i	$0.866872\pi$
$3$	0.310785	−	1.70394i	0.179432	−	0.983770i
$3$	0.310785	−	1.70394i	0.179432	−	0.983770i
$4$	0.955758	−	1.65542i	0.477879	−	0.827711i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.485175	+	0.173367i	−0.198072	+	0.0707769i
$7$	−2.64436	+	0.0857253i	−0.999475	+	0.0324011i
$7$	−2.64436	+	0.0857253i	−0.999475	+	0.0324011i
$8$	−1.16353			−0.411369
$9$	−2.80683	−	1.05912i	−0.935608	−	0.353040i
$10$	0.148731	+	0.257610i	0.0470328	+	0.0814633i
$11$	4.84852			1.46188			0.730942	−	0.682440i	$-0.239081\pi$
$11$	4.84852			1.46188			0.730942	+	0.682440i	$0.239081\pi$
$12$	−2.52370	−	2.14304i	−0.728531	−	0.618641i
$13$	−2.59263	−	4.49056i	−0.719066	−	1.24546i	−0.961370	−	0.275258i	$-0.911237\pi$
$13$	−2.59263	−	4.49056i	−0.719066	−	1.24546i	0.242305	−	0.970200i	$-0.422097\pi$
$14$	0.415382	+	0.668463i	0.111016	+	0.178654i
$15$	−0.310785	+	1.70394i	−0.0802444	+	0.439955i
$16$	−1.73846	−	3.01111i	−0.434616	−	0.752777i
$17$	1.80070	+	3.11891i	0.436734	+	0.756446i	0.997435	−	0.0715721i	$-0.0228016\pi$
$17$	1.80070	+	3.11891i	0.436734	+	0.756446i	−0.560701	+	0.828018i	$0.689468\pi$
$18$	0.144623	+	0.880589i	0.0340879	+	0.207557i
$19$	−2.03033	+	3.51663i	−0.465789	+	0.806770i	−0.999237	−	0.0390629i	$-0.987563\pi$
$19$	−2.03033	+	3.51663i	−0.465789	+	0.806770i	0.533448	+	0.845833i	$0.320896\pi$
$20$	−0.955758	+	1.65542i	−0.213714	+	0.370164i
$21$	−0.675758	+	4.53248i	−0.147462	+	0.989068i
$22$	−0.721125	−	1.24902i	−0.153744	−	0.266293i
$23$	0.983576			0.205090			0.102545	−	0.994728i	$-0.467301\pi$
$23$	0.983576			0.205090			0.102545	+	0.994728i	$0.467301\pi$
$24$	−0.361607	+	1.98258i	−0.0738127	+	0.404693i
$25$	1.00000			0.200000
$26$	−0.771208	+	1.33577i	−0.151246	+	0.261966i
$27$	−2.67699	+	4.45350i	−0.515188	+	0.857077i
$28$	−2.38546	+	4.45947i	−0.450809	+	0.842760i
$29$	2.30352	−	3.98981i	0.427753	−	0.740890i	−0.568920	−	0.822393i	$-0.692639\pi$
$29$	2.30352	−	3.98981i	0.427753	−	0.740890i	0.996673	+	0.0815030i	$0.0259720\pi$
$30$	0.485175	−	0.173367i	0.0885804	−	0.0316524i
$31$	3.60041	−	6.23609i	0.646652	−	1.12003i	−0.337265	−	0.941410i	$-0.609502\pi$
$31$	3.60041	−	6.23609i	0.646652	−	1.12003i	0.983917	−	0.178625i	$-0.0571649\pi$
$32$	−1.68065	+	2.91098i	−0.297100	+	0.514593i
$33$	1.50685	−	8.26159i	0.262308	−	1.43816i
$34$	0.535640	−	0.927756i	0.0918615	−	0.159109i
$35$	2.64436	−	0.0857253i	0.446979	−	0.0144902i
$36$	−4.43593	+	3.63422i	−0.739322	+	0.605703i
$37$	3.25248	−	5.63347i	0.534705	−	0.926137i	−0.464472	−	0.885588i	$-0.653756\pi$
$37$	3.25248	−	5.63347i	0.534705	−	0.926137i	0.999178	−	0.0405489i	$-0.0129107\pi$
$38$	1.20789			0.195946
$39$	−8.45740	+	3.02208i	−1.35427	+	0.483921i
$40$	1.16353			0.183970
$41$	−0.298439	−	0.516911i	−0.0466083	−	0.0807280i	0.841780	−	0.539821i	$-0.181508\pi$
$41$	−0.298439	−	0.516911i	−0.0466083	−	0.0807280i	−0.888388	+	0.459093i	$0.848175\pi$
$42$	1.26812	−	0.500038i	0.195674	−	0.0771575i
$43$	0.0565258	−	0.0979056i	0.00862010	−	0.0149305i	−0.861683	−	0.507447i	$-0.830589\pi$
$43$	0.0565258	−	0.0979056i	0.00862010	−	0.0149305i	0.870303	+	0.492516i	$0.163923\pi$
$44$	4.63401	−	8.02634i	0.698603	−	1.21002i
$45$	2.80683	+	1.05912i	0.418417	+	0.157884i
$46$	−0.146288	−	0.253378i	−0.0215690	−	0.0373586i
$47$	−3.57890	−	6.19883i	−0.522036	−	0.904192i	−0.999671	−	0.0256342i	$-0.991839\pi$
$47$	−3.57890	−	6.19883i	−0.522036	−	0.904192i	0.477636	−	0.878558i	$-0.341494\pi$
$48$	−5.67104	+	2.02643i	−0.818544	+	0.292490i
$49$	6.98530	−	0.453377i	0.997900	−	0.0647682i
$50$	−0.148731	−	0.257610i	−0.0210337	−	0.0364315i
$51$	5.87406	−	2.09898i	0.822534	−	0.293916i
$52$	−9.91170			−1.37451
$53$	4.78827	+	8.29352i	0.657719	+	1.13920i	0.981205	+	0.192970i	$0.0618119\pi$
$53$	4.78827	+	8.29352i	0.657719	+	1.13920i	−0.323486	+	0.946233i	$0.604855\pi$
$54$	1.54542	+	0.0272455i	0.210305	+	0.00370764i
$55$	−4.84852			−0.653774
$56$	3.07679	−	0.0997437i	0.411153	−	0.0133288i
$57$	5.36113	+	4.55247i	0.710099	+	0.602990i
$58$	−1.37042			−0.179945
$59$	3.75057	−	6.49618i	0.488283	−	0.845731i	−0.511626	−	0.859208i	$-0.670957\pi$
$59$	3.75057	−	6.49618i	0.488283	−	0.845731i	0.999909	+	0.0134771i	$0.00429003\pi$
$60$	2.52370	+	2.14304i	0.325809	+	0.276665i
$61$	7.49581	+	12.9831i	0.959740	+	1.66232i	0.723129	+	0.690713i	$0.242703\pi$
$61$	7.49581	+	12.9831i	0.959740	+	1.66232i	0.236611	+	0.971604i	$0.423963\pi$
$62$	−2.14197			−0.272030
$63$	7.51306	+	2.56008i	0.946556	+	0.322539i
$64$	−5.95400			−0.744249
$65$	2.59263	+	4.49056i	0.321576	+	0.556986i
$66$	−2.35238	+	0.840575i	−0.289558	+	0.103468i
$67$	3.78548	−	6.55664i	0.462470	−	0.801021i	−0.536613	−	0.843828i	$-0.680297\pi$
$67$	3.78548	−	6.55664i	0.462470	−	0.801021i	0.999083	+	0.0428067i	$0.0136300\pi$
$68$	6.88414			0.834825
$69$	0.305681	−	1.67595i	0.0367996	−	0.201761i
$70$	−0.415382	−	0.668463i	−0.0496477	−	0.0798966i
$71$	10.2073			1.21138			0.605690	−	0.795701i	$-0.292897\pi$
$71$	10.2073			1.21138			0.605690	+	0.795701i	$0.292897\pi$
$72$	3.26582	+	1.23231i	0.384880	+	0.145229i
$73$	−1.67879	−	2.90775i	−0.196487	−	0.340326i	0.750900	−	0.660416i	$-0.229620\pi$
$73$	−1.67879	−	2.90775i	−0.196487	−	0.340326i	−0.947387	+	0.320090i	$0.896287\pi$
$74$	−1.93498			−0.224937
$75$	0.310785	−	1.70394i	0.0358864	−	0.196754i
$76$	3.88100	+	6.72209i	0.445182	+	0.771077i
$77$	−12.8212	+	0.415641i	−1.46112	+	0.0473667i
$78$	2.03639	+	1.72923i	0.230576	+	0.195797i
$79$	−2.59268	−	4.49066i	−0.291699	−	0.505238i	0.682512	−	0.730874i	$-0.260887\pi$
$79$	−2.59268	−	4.49066i	−0.291699	−	0.505238i	−0.974212	+	0.225636i	$0.927554\pi$
$80$	1.73846	+	3.01111i	0.194366	+	0.336652i
$81$	6.75654	+	5.94552i	0.750726	+	0.660614i
$82$	−0.0887742	+	0.153761i	−0.00980347	+	0.0169801i
$83$	−5.45891	+	9.45512i	−0.599194	+	1.03783i	0.393747	+	0.919219i	$0.371179\pi$
$83$	−5.45891	+	9.45512i	−0.599194	+	1.03783i	−0.992940	+	0.118615i	$0.962155\pi$
$84$	6.85730	+	5.45062i	0.748193	+	0.594711i
$85$	−1.80070	−	3.11891i	−0.195314	−	0.338293i
$86$	−0.0336285			−0.00362626
$87$	−6.08250	−	5.16504i	−0.652113	−	0.553750i
$88$	−5.64138			−0.601373
$89$	−7.64065	+	13.2340i	−0.809907	+	1.40280i	0.103021	+	0.994679i	$0.467149\pi$
$89$	−7.64065	+	13.2340i	−0.809907	+	1.40280i	−0.912928	+	0.408121i	$0.866184\pi$
$90$	−0.144623	−	0.880589i	−0.0152446	−	0.0928222i
$91$	7.24080	+	11.6524i	0.759042	+	1.22151i
$92$	0.940061	−	1.62823i	0.0980081	−	0.169755i
$93$	−9.50697	−	8.07296i	−0.985827	−	0.837127i
$94$	−1.06458	+	1.84392i	−0.109804	+	0.190185i
$95$	2.03033	−	3.51663i	0.208307	−	0.360799i
$96$	4.43781	+	3.76842i	0.452932	+	0.384613i
$97$	6.85013	−	11.8648i	0.695525	−	1.20469i	−0.274478	−	0.961593i	$-0.588505\pi$
$97$	6.85013	−	11.8648i	0.695525	−	1.20469i	0.970003	−	0.243092i	$-0.0781616\pi$
$98$	−1.15572	−	1.73205i	−0.116746	−	0.174963i
$99$	−13.6089	−	5.13516i	−1.36775	−	0.516103i
$100$	0.955758	−	1.65542i	0.0955758	−	0.165542i
$101$	0.893587			0.0889152			0.0444576	−	0.999011i	$-0.485844\pi$
$101$	0.893587			0.0889152			0.0444576	+	0.999011i	$0.485844\pi$
$102$	−1.41437	−	1.20103i	−0.140044	−	0.118920i
$103$	−0.894109			−0.0880992			−0.0440496	−	0.999029i	$-0.514026\pi$
$103$	−0.894109			−0.0880992			−0.0440496	+	0.999029i	$0.514026\pi$
$104$	3.01659	+	5.22489i	0.295801	+	0.512343i
$105$	0.675758	−	4.53248i	0.0659472	−	0.442325i
$106$	1.42433	−	2.46701i	0.138343	−	0.239617i
$107$	3.75665	−	6.50670i	0.363169	−	0.629027i	−0.625312	−	0.780375i	$-0.715028\pi$
$107$	3.75665	−	6.50670i	0.363169	−	0.629027i	0.988480	+	0.151348i	$0.0483615\pi$
$108$	4.81387	+	8.68803i	0.463215	+	0.836006i
$109$	1.97286	+	3.41710i	0.188966	+	0.327299i	0.944906	−	0.327342i	$-0.106153\pi$
$109$	1.97286	+	3.41710i	0.188966	+	0.327299i	−0.755940	+	0.654641i	$0.772820\pi$
$110$	0.721125	+	1.24902i	0.0687565	+	0.119090i
$111$	−8.58827	−	7.29284i	−0.815163	−	0.692206i
$112$	4.85526	+	7.81343i	0.458779	+	0.738300i
$113$	8.37945	+	14.5136i	0.788272	+	1.36533i	0.927025	+	0.375001i	$0.122357\pi$
$113$	8.37945	+	14.5136i	0.788272	+	1.36533i	−0.138752	+	0.990327i	$0.544309\pi$
$114$	0.375394	−	2.05817i	0.0351589	−	0.192765i
$115$	−0.983576			−0.0917189
$116$	−4.40322	−	7.62659i	−0.408828	−	0.708111i
$117$	2.52101	+	15.3501i	0.233068	+	1.41912i
$118$	−2.23130			−0.205408
$119$	−5.02908	−	8.09316i	−0.461015	−	0.741898i
$120$	0.361607	−	1.98258i	0.0330100	−	0.180984i
$121$	12.5081			1.13710
$122$	2.22972	−	3.86198i	0.201869	−	0.349647i
$123$	−0.973536	+	0.347874i	−0.0877808	+	0.0313667i
$124$	−6.88224	−	11.9204i	−0.618043	−	1.07048i
$125$	−1.00000			−0.0894427
$126$	−0.457923	−	2.31620i	−0.0407951	−	0.206343i
$127$	2.53868			0.225271			0.112636	−	0.993636i	$-0.464071\pi$
$127$	2.53868			0.225271			0.112636	+	0.993636i	$0.464071\pi$
$128$	4.24685	+	7.35576i	0.375372	+	0.650164i
$129$	−0.149258	−	0.126744i	−0.0131414	−	0.0111592i
$130$	0.771208	−	1.33577i	0.0676394	−	0.117155i
$131$	−18.3245			−1.60101			−0.800507	−	0.599323i	$-0.795437\pi$
$131$	−18.3245			−1.60101			−0.800507	+	0.599323i	$0.795437\pi$
$132$	−12.2362	−	10.3905i	−1.06503	−	0.904381i
$133$	5.06746	−	9.47329i	0.439404	−	0.821439i
$134$	−2.25207			−0.194549
$135$	2.67699	−	4.45350i	0.230399	−	0.383297i
$136$	−2.09517	−	3.62893i	−0.179659	−	0.311178i
$137$	4.83191			0.412818			0.206409	−	0.978466i	$-0.433822\pi$
$137$	4.83191			0.412818			0.206409	+	0.978466i	$0.433822\pi$
$138$	−0.477206	+	0.170520i	−0.0406225	+	0.0145156i
$139$	2.74078	+	4.74717i	0.232470	+	0.402650i	0.958534	−	0.284977i	$-0.0919860\pi$
$139$	2.74078	+	4.74717i	0.232470	+	0.402650i	−0.726065	+	0.687627i	$0.758653\pi$
$140$	2.38546	−	4.45947i	0.201608	−	0.376894i
$141$	−11.6747	+	4.17172i	−0.983187	+	0.351322i
$142$	−1.51814	−	2.62949i	−0.127399	−	0.220662i
$143$	−12.5704	−	21.7726i	−1.05119	−	1.82071i
$144$	1.69044	+	10.2929i	0.140870	+	0.857741i
$145$	−2.30352	+	3.98981i	−0.191297	+	0.331336i
$146$	−0.499376	+	0.864944i	−0.0413286	+	0.0715833i
$147$	1.39840	−	12.0434i	0.115338	−	0.993326i
$148$	−6.21718	−	10.7685i	−0.511049	−	0.885163i
$149$	0.485413			0.0397665			0.0198833	−	0.999802i	$-0.493671\pi$
$149$	0.485413			0.0397665			0.0198833	+	0.999802i	$0.493671\pi$
$150$	−0.485175	+	0.173367i	−0.0396143	+	0.0141554i
$151$	−14.6157			−1.18941			−0.594706	−	0.803943i	$-0.702732\pi$
$151$	−14.6157			−1.18941			−0.594706	+	0.803943i	$0.702732\pi$
$152$	2.36234	−	4.09169i	0.191611	−	0.331880i
$153$	−1.75096	−	10.6614i	−0.141557	−	0.861922i
$154$	2.01399	+	3.24105i	0.162292	+	0.261172i
$155$	−3.60041	+	6.23609i	−0.289192	+	0.500895i
$156$	−3.08041	+	16.8889i	−0.246630	+	1.35220i
$157$	−5.63107	+	9.75331i	−0.449409	+	0.778399i	−0.998348	−	0.0574638i	$-0.981699\pi$
$157$	−5.63107	+	9.75331i	−0.449409	+	0.778399i	0.548939	+	0.835862i	$0.315032\pi$
$158$	−0.771224	+	1.33580i	−0.0613553	+	0.106270i
$159$	15.6198	−	5.58142i	1.23873	−	0.442635i
$160$	1.68065	−	2.91098i	0.132867	−	0.230133i
$161$	−2.60093	+	0.0843173i	−0.204982	+	0.00664514i
$162$	0.526717	−	2.62483i	0.0413828	−	0.206226i
$163$	−6.83343	+	11.8358i	−0.535236	+	0.927055i	0.463916	+	0.885879i	$0.346444\pi$
$163$	−6.83343	+	11.8358i	−0.535236	+	0.927055i	−0.999152	+	0.0411762i	$0.986889\pi$
$164$	−1.14094			−0.0890926
$165$	−1.50685	+	8.26159i	−0.117308	+	0.643164i
$166$	3.24764			0.252066
$167$	−1.43443	−	2.48450i	−0.110999	−	0.192256i	0.805174	−	0.593038i	$-0.202072\pi$
$167$	−1.43443	−	2.48450i	−0.110999	−	0.192256i	−0.916173	+	0.400782i	$0.868738\pi$
$168$	0.786262	−	5.27366i	0.0606614	−	0.406872i
$169$	−6.94344	+	12.0264i	−0.534111	+	0.925107i
$170$	−0.535640	+	0.927756i	−0.0410817	+	0.0711556i
$171$	9.42330	−	7.72021i	0.720618	−	0.590379i
$172$	−0.108050	−	0.187148i	−0.00823874	−	0.0142699i
$173$	−2.57731	−	4.46403i	−0.195949	−	0.339394i	0.751262	−	0.660004i	$-0.229445\pi$
$173$	−2.57731	−	4.46403i	−0.195949	−	0.339394i	−0.947211	+	0.320610i	$0.896112\pi$
$174$	−0.425906	+	2.33511i	−0.0322878	+	0.177024i
$175$	−2.64436	+	0.0857253i	−0.199895	+	0.00648022i
$176$	−8.42897	−	14.5994i	−0.635358	−	1.10047i
$177$	−9.90349	−	8.40967i	−0.744392	−	0.632110i
$178$	4.54560			0.340707
$179$	7.35505	+	12.7393i	0.549742	+	0.952182i	0.998292	+	0.0584237i	$0.0186074\pi$
$179$	7.35505	+	12.7393i	0.549742	+	0.952182i	−0.448550	+	0.893758i	$0.648059\pi$
$180$	4.43593	−	3.63422i	0.330635	−	0.270879i
$181$	12.6894			0.943192			0.471596	−	0.881815i	$-0.343678\pi$
$181$	12.6894			0.943192			0.471596	+	0.881815i	$0.343678\pi$
$182$	1.92484	−	3.59837i	0.142679	−	0.266729i
$183$	24.4520	−	8.73745i	1.80755	−	0.645891i
$184$	−1.14442			−0.0843675
$185$	−3.25248	+	5.63347i	−0.239127	+	0.414181i
$186$	−0.665692	+	3.64979i	−0.0488109	+	0.267615i
$187$	8.73074	+	15.1221i	0.638455	+	1.10584i
$188$	−13.6822			−0.997880
$189$	6.69717	−	12.0062i	0.487147	−	0.873320i
$190$	−1.20789			−0.0876295
$191$	−4.46643	−	7.73608i	−0.323179	−	0.559763i	0.657963	−	0.753050i	$-0.271418\pi$
$191$	−4.46643	−	7.73608i	−0.323179	−	0.559763i	−0.981142	+	0.193287i	$0.938085\pi$
$192$	−1.85041	+	10.1453i	−0.133542	+	0.732171i
$193$	−0.852021	+	1.47574i	−0.0613298	+	0.106226i	−0.895060	−	0.445946i	$-0.852867\pi$
$193$	−0.852021	+	1.47574i	−0.0613298	+	0.106226i	0.833730	+	0.552172i	$0.186201\pi$
$194$	−4.07530			−0.292590
$195$	8.45740	−	3.02208i	0.605647	−	0.216416i
$196$	5.92573	−	11.9969i	0.423266	−	0.856924i
$197$	−16.0684			−1.14483			−0.572414	−	0.819965i	$-0.693993\pi$
$197$	−16.0684			−1.14483			−0.572414	+	0.819965i	$0.693993\pi$
$198$	0.701206	+	4.26955i	0.0498325	+	0.303424i
$199$	−4.15353	−	7.19412i	−0.294436	−	0.509977i	0.680418	−	0.732824i	$-0.261798\pi$
$199$	−4.15353	−	7.19412i	−0.294436	−	0.509977i	−0.974853	+	0.222847i	$0.928465\pi$
$200$	−1.16353			−0.0822738
$201$	−9.99566	−	8.48794i	−0.705039	−	0.598693i
$202$	−0.132904	−	0.230196i	−0.00935109	−	0.0161966i
$203$	−5.74931	+	10.7480i	−0.403523	+	0.754360i
$204$	2.13949	−	11.7302i	0.149794	−	0.821276i
$205$	0.298439	+	0.516911i	0.0208439	+	0.0361027i
$206$	0.132982	+	0.230331i	0.00926528	+	0.0160479i
$207$	−2.76073	−	1.04172i	−0.191884	−	0.0724048i
$208$	−9.01438	+	15.6134i	−0.625035	+	1.08259i
$209$	−9.84408	+	17.0504i	−0.680929	+	1.17940i
$210$	−1.26812	+	0.500038i	−0.0875083	+	0.0345059i
$211$	7.63592	+	13.2258i	0.525679	+	0.910502i	0.999553	+	0.0299095i	$0.00952191\pi$
$211$	7.63592	+	13.2258i	0.525679	+	0.910502i	−0.473874	+	0.880593i	$0.657145\pi$
$212$	18.3057			1.25724
$213$	3.17227	−	17.3926i	0.217360	−	1.19172i
$214$	−2.23492			−0.152776
$215$	−0.0565258	+	0.0979056i	−0.00385503	+	0.00667710i
$216$	3.11476	−	5.18177i	0.211932	−	0.352575i
$217$	−8.98619	+	16.7991i	−0.610022	+	1.14040i
$218$	0.586852	−	1.01646i	0.0397466	−	0.0688431i
$219$	−5.47637	+	1.95687i	−0.370059	+	0.132233i
$220$	−4.63401	+	8.02634i	−0.312425	+	0.541136i
$221$	9.33710	−	16.1723i	0.628081	−	1.08787i
$222$	−0.601363	+	3.29709i	−0.0403608	+	0.221286i
$223$	−2.63572	+	4.56520i	−0.176501	+	0.305709i	−0.940680	−	0.339296i	$-0.889811\pi$
$223$	−2.63572	+	4.56520i	−0.176501	+	0.305709i	0.764179	+	0.645005i	$0.223145\pi$
$224$	4.19471	−	7.84175i	0.280271	−	0.523949i
$225$	−2.80683	−	1.05912i	−0.187122	−	0.0706079i
$226$	2.49257	−	4.31725i	0.165803	−	0.287179i
$227$	−15.4848			−1.02777			−0.513883	−	0.857860i	$-0.671793\pi$
$227$	−15.4848			−1.02777			−0.513883	+	0.857860i	$0.671793\pi$
$228$	12.6602	−	4.52387i	0.838443	−	0.299601i
$229$	−12.8356			−0.848199			−0.424100	−	0.905616i	$-0.639409\pi$
$229$	−12.8356			−0.848199			−0.424100	+	0.905616i	$0.639409\pi$
$230$	0.146288	+	0.253378i	0.00964595	+	0.0167073i
$231$	−3.27642	+	21.9758i	−0.215573	+	1.44590i
$232$	−2.68021	+	4.64226i	−0.175964	+	0.304779i
$233$	−1.98735	+	3.44220i	−0.130196	+	0.225506i	−0.923752	−	0.382991i	$-0.874894\pi$
$233$	−1.98735	+	3.44220i	−0.130196	+	0.225506i	0.793556	+	0.608497i	$0.208227\pi$
$234$	3.57939	−	2.93248i	0.233992	−	0.191702i
$235$	3.57890	+	6.19883i	0.233461	+	0.404367i
$236$	−7.16928	−	12.4176i	−0.466681	−	0.808314i
$237$	−8.45758	+	3.02215i	−0.549379	+	0.196309i
$238$	−1.33689	+	2.49924i	−0.0866580	+	0.162002i
$239$	−12.7164	−	22.0255i	−0.822558	−	1.42471i	−0.903771	−	0.428016i	$-0.859213\pi$
$239$	−12.7164	−	22.0255i	−0.822558	−	1.42471i	0.0812127	−	0.996697i	$-0.474121\pi$
$240$	5.67104	−	2.02643i	0.366064	−	0.130806i
$241$	−4.34960			−0.280183			−0.140091	−	0.990139i	$-0.544740\pi$
$241$	−4.34960			−0.280183			−0.140091	+	0.990139i	$0.544740\pi$
$242$	−1.86035	−	3.22221i	−0.119588	−	0.207132i
$243$	12.2306	−	9.66495i	0.784596	−	0.620007i
$244$	28.6567			1.83456
$245$	−6.98530	+	0.453377i	−0.446275	+	0.0289652i
$246$	0.234411	+	0.199053i	0.0149455	+	0.0126911i
$247$	21.0555			1.33973
$248$	−4.18917	+	7.25586i	−0.266013	+	0.460747i
$249$	14.4144	+	12.2402i	0.913476	+	0.775690i
$250$	0.148731	+	0.257610i	0.00940657	+	0.0162927i
$251$	1.40554			0.0887172			0.0443586	−	0.999016i	$-0.485876\pi$
$251$	1.40554			0.0887172			0.0443586	+	0.999016i	$0.485876\pi$
$252$	11.4187	−	9.99046i	0.719309	−	0.629340i
$253$	4.76889			0.299817
$254$	−0.377580	−	0.653987i	−0.0236915	−	0.0410348i
$255$	−5.87406	+	2.09898i	−0.367848	+	0.131443i
$256$	−4.69072	+	8.12456i	−0.293170	+	0.507785i
$257$	8.20043			0.511529			0.255765	−	0.966739i	$-0.417673\pi$
$257$	8.20043			0.511529			0.255765	+	0.966739i	$0.417673\pi$
$258$	−0.0104512	+	0.0573010i	−0.000650666	+	0.00356741i
$259$	−8.11782	+	15.1758i	−0.504417	+	0.942975i
$260$	9.91170			0.614698
$261$	−10.6913	+	8.75901i	−0.661773	+	0.542169i
$262$	2.72541	+	4.72055i	0.168377	+	0.291637i
$263$	23.4680			1.44710			0.723549	−	0.690273i	$-0.242510\pi$
$263$	23.4680			1.44710			0.723549	+	0.690273i	$0.242510\pi$
$264$	−1.75326	+	9.61258i	−0.107906	+	0.591613i
$265$	−4.78827	−	8.29352i	−0.294141	−	0.509467i
$266$	−3.19410	+	0.103547i	−0.195843	+	0.00634885i
$267$	20.1753	+	17.1321i	1.23471	+	1.04847i
$268$	−7.23601	−	12.5331i	−0.442009	−	0.765583i
$269$	4.35529	+	7.54358i	0.265547	+	0.459940i	0.967707	−	0.252079i	$-0.0811142\pi$
$269$	4.35529	+	7.54358i	0.265547	+	0.459940i	−0.702160	+	0.712019i	$0.747781\pi$
$270$	−1.54542	−	0.0272455i	−0.0940511	−	0.00165811i
$271$	7.28571	−	12.6192i	0.442575	−	0.766563i	−0.555304	−	0.831647i	$-0.687398\pi$
$271$	7.28571	−	12.6192i	0.442575	−	0.766563i	0.997880	+	0.0650842i	$0.0207316\pi$
$272$	6.26091	−	10.8442i	0.379624	−	0.657527i
$273$	22.1054	−	8.71649i	1.33788	−	0.527546i
$274$	−0.718654	−	1.24475i	−0.0434155	−	0.0751979i
$275$	4.84852			0.292377
$276$	−2.48225	−	2.10784i	−0.149414	−	0.126877i
$277$	−5.09267			−0.305989			−0.152994	−	0.988227i	$-0.548892\pi$
$277$	−5.09267			−0.305989			−0.152994	+	0.988227i	$0.548892\pi$
$278$	0.815277	−	1.41210i	0.0488971	−	0.0846922i
$279$	−16.7105	+	13.6904i	−1.00043	+	0.819620i
$280$	−3.07679	+	0.0997437i	−0.183873	+	0.00596083i
$281$	−4.49611	+	7.78750i	−0.268216	+	0.464563i	−0.968401	−	0.249398i	$-0.919767\pi$
$281$	−4.49611	+	7.78750i	−0.268216	+	0.464563i	0.700185	+	0.713961i	$0.253101\pi$
$282$	2.81106	+	2.38705i	0.167396	+	0.142147i
$283$	3.12203	−	5.40751i	0.185585	−	0.321443i	−0.758188	−	0.652036i	$-0.773915\pi$
$283$	3.12203	−	5.40751i	0.185585	−	0.321443i	0.943774	+	0.330593i	$0.107249\pi$
$284$	9.75569	−	16.8973i	0.578893	−	1.00267i
$285$	−5.36113	−	4.55247i	−0.317566	−	0.269665i
$286$	−3.73922	+	6.47651i	−0.221104	+	0.382964i
$287$	0.833493	+	1.34132i	0.0491995	+	0.0791754i
$288$	7.80037	−	6.39059i	0.459641	−	0.376569i
$289$	2.01494	−	3.48998i	0.118526	−	0.205293i
$290$	1.37042			0.0804737
$291$	−18.0879	−	15.3596i	−1.06033	−	0.900396i
$292$	−6.41806			−0.375589
$293$	14.4502	+	25.0286i	0.844192	+	1.46218i	0.886321	+	0.463072i	$0.153253\pi$
$293$	14.4502	+	25.0286i	0.844192	+	1.46218i	−0.0421288	+	0.999112i	$0.513414\pi$
$294$	−3.31049	+	1.43099i	−0.193072	+	0.0834571i
$295$	−3.75057	+	6.49618i	−0.218367	+	0.378222i
$296$	−3.78435	+	6.55469i	−0.219961	+	0.380984i
$297$	−12.9795	+	21.5929i	−0.753144	+	1.25295i
$298$	−0.0721959	−	0.125047i	−0.00418219	−	0.00724377i
$299$	−2.55005	−	4.41681i	−0.147473	−	0.255431i
$300$	−2.52370	−	2.14304i	−0.145706	−	0.123728i
$301$	−0.141082	+	0.263743i	−0.00813181	+	0.0152019i
$302$	2.17381	+	3.76516i	0.125089	+	0.216660i
$303$	0.277713	−	1.52262i	0.0159542	−	0.0874721i
$304$	14.1186			0.809757
$305$	−7.49581	−	12.9831i	−0.429209	−	0.743411i
$306$	−2.48605	+	2.03674i	−0.142118	+	0.116433i
$307$	24.3854			1.39175			0.695873	−	0.718165i	$-0.255018\pi$
$307$	24.3854			1.39175			0.695873	+	0.718165i	$0.255018\pi$
$308$	−11.5659	+	21.6218i	−0.659031	+	1.23202i
$309$	−0.277876	+	1.52351i	−0.0158078	+	0.0866694i
$310$	2.14197			0.121656
$311$	−8.84784	+	15.3249i	−0.501715	+	0.868996i	0.498283	+	0.867014i	$0.333964\pi$
$311$	−8.84784	+	15.3249i	−0.501715	+	0.868996i	−0.999998	+	0.00198124i	$0.999369\pi$
$312$	9.84041	−	3.51627i	0.557104	−	0.199070i
$313$	−0.260533	−	0.451256i	−0.0147262	−	0.0255065i	0.858568	−	0.512699i	$-0.171354\pi$
$313$	−0.260533	−	0.451256i	−0.0147262	−	0.0255065i	−0.873295	+	0.487193i	$0.838021\pi$
$314$	3.35006			0.189055
$315$	−7.51306	−	2.56008i	−0.423313	−	0.144244i
$316$	−9.91191			−0.557588
$317$	9.44066	+	16.3517i	0.530241	+	0.918404i	0.999378	+	0.0352781i	$0.0112317\pi$
$317$	9.44066	+	16.3517i	0.530241	+	0.918404i	−0.469137	+	0.883125i	$0.655435\pi$
$318$	−3.76097	−	3.19368i	−0.210905	−	0.179092i
$319$	11.1687	−	19.3447i	0.625325	−	1.08309i
$320$	5.95400			0.332838
$321$	−9.91952	−	8.42329i	−0.553654	−	0.470142i
$322$	0.408560	+	0.657484i	0.0227681	+	0.0366401i
$323$	−14.6241			−0.813704
$324$	16.3000	−	5.50243i	0.905553	−	0.305691i
$325$	−2.59263	−	4.49056i	−0.143813	−	0.249092i
$326$	4.06537			0.225160
$327$	6.43567	−	2.29966i	0.355893	−	0.127171i
$328$	0.347242	+	0.601440i	0.0191732	+	0.0332090i
$329$	9.99529	+	16.0851i	0.551058	+	0.886803i
$330$	2.35238	−	0.840575i	0.129494	−	0.0462721i
$331$	−13.1393	−	22.7580i	−0.722202	−	1.25089i	−0.960115	−	0.279604i	$-0.909797\pi$
$331$	−13.1393	−	22.7580i	−0.722202	−	1.25089i	0.237913	−	0.971286i	$-0.423537\pi$
$332$	10.4348	+	18.0736i	0.572684	+	0.991918i
$333$	−15.0957	+	12.3674i	−0.827237	+	0.677729i
$334$	−0.426687	+	0.739044i	−0.0233473	+	0.0404387i
$335$	−3.78548	+	6.55664i	−0.206823	+	0.358228i
$336$	14.8226	−	5.84477i	0.808637	−	0.318858i
$337$	11.9856	+	20.7597i	0.652899	+	1.13085i	0.982416	+	0.186705i	$0.0597808\pi$
$337$	11.9856	+	20.7597i	0.652899	+	1.13085i	−0.329517	+	0.944150i	$0.606886\pi$
$338$	4.13082			0.224687
$339$	27.3346	−	9.76746i	1.48461	−	0.530496i
$340$	−6.88414			−0.373345
$341$	17.4566	−	30.2358i	0.945330	−	1.63736i
$342$	−3.39033	−	1.27930i	−0.183328	−	0.0691765i
$343$	−18.4328	+	1.79771i	−0.995278	+	0.0970673i
$344$	−0.0657693	+	0.113916i	−0.00354604	+	0.00614193i
$345$	−0.305681	+	1.67595i	−0.0164573	+	0.0902304i
$346$	−0.766650	+	1.32788i	−0.0412154	+	0.0713871i
$347$	3.68239	−	6.37809i	0.197681	−	0.342394i	−0.750095	−	0.661330i	$-0.769992\pi$
$347$	3.68239	−	6.37809i	0.197681	−	0.342394i	0.947776	+	0.318936i	$0.103326\pi$
$348$	−14.3637	+	5.13259i	−0.769976	+	0.275135i
$349$	8.74591	−	15.1484i	0.468158	−	0.810873i	−0.531180	−	0.847259i	$-0.678251\pi$
$349$	8.74591	−	15.1484i	0.468158	−	0.810873i	0.999338	+	0.0363861i	$0.0115846\pi$
$350$	0.415382	+	0.668463i	0.0222031	+	0.0357308i
$351$	26.9392	+	0.474934i	1.43791	+	0.0253501i
$352$	−8.14868	+	14.1139i	−0.434326	+	0.752275i
$353$	30.5114			1.62396			0.811979	−	0.583687i	$-0.198390\pi$
$353$	30.5114			1.62396			0.811979	+	0.583687i	$0.198390\pi$
$354$	−0.693456	+	3.80201i	−0.0368568	+	0.202075i
$355$	−10.2073			−0.541746
$356$	14.6052	+	25.2970i	0.774075	+	1.34074i
$357$	−15.3532	+	6.05402i	−0.812579	+	0.320413i
$358$	2.18785	−	3.78946i	0.115631	−	0.200279i
$359$	−7.90187	+	13.6864i	−0.417045	+	0.722343i	−0.995641	−	0.0932716i	$-0.970268\pi$
$359$	−7.90187	+	13.6864i	−0.417045	+	0.722343i	0.578596	+	0.815614i	$0.303601\pi$
$360$	−3.26582	−	1.23231i	−0.172124	−	0.0649486i
$361$	1.25555	+	2.17467i	0.0660814	+	0.114456i
$362$	−1.88730	−	3.26890i	−0.0991942	−	0.171809i
$363$	3.88734	−	21.3131i	0.204032	−	1.11865i
$364$	26.2101	−	0.849684i	1.37378	−	0.0445355i
$365$	1.67879	+	2.90775i	0.0878718	+	0.152198i
$366$	−5.88762	−	4.99955i	−0.307751	−	0.261331i
$367$	24.7914			1.29410			0.647051	−	0.762447i	$-0.276002\pi$
$367$	24.7914			1.29410			0.647051	+	0.762447i	$0.276002\pi$
$368$	−1.70991	−	2.96165i	−0.0891353	−	0.154387i
$369$	0.290195	+	1.76696i	0.0151070	+	0.0919844i
$370$	1.93498			0.100595
$371$	−13.3729	−	21.5206i	−0.694285	−	1.11729i
$372$	−22.4505	+	8.02225i	−1.16401	+	0.415934i
$373$	−17.3302			−0.897325			−0.448662	−	0.893701i	$-0.648099\pi$
$373$	−17.3302			−0.897325			−0.448662	+	0.893701i	$0.648099\pi$
$374$	2.59706	−	4.49824i	0.134291	−	0.232599i
$375$	−0.310785	+	1.70394i	−0.0160489	+	0.0879911i
$376$	4.16414	+	7.21250i	0.214749	+	0.371956i
$377$	−23.8887			−1.23033
$378$	−4.08898	+	0.0604344i	−0.210314	+	0.00310841i
$379$	−10.3256			−0.530391			−0.265196	−	0.964195i	$-0.585437\pi$
$379$	−10.3256			−0.530391			−0.265196	+	0.964195i	$0.585437\pi$
$380$	−3.88100	−	6.72209i	−0.199091	−	0.344836i
$381$	0.788983	−	4.32575i	0.0404208	−	0.221615i
$382$	−1.32859	+	2.30119i	−0.0679767	+	0.117739i
$383$	5.83247			0.298025			0.149013	−	0.988835i	$-0.452391\pi$
$383$	5.83247			0.298025			0.149013	+	0.988835i	$0.452391\pi$
$384$	13.8536	−	4.95032i	0.706965	−	0.252620i
$385$	12.8212	−	0.415641i	0.653431	−	0.0211830i
$386$	0.506887			0.0257999
$387$	−0.262352	+	0.214936i	−0.0133361	+	0.0109258i
$388$	−13.0941	−	22.6797i	−0.664754	−	1.15139i
$389$	−30.8805			−1.56571			−0.782853	−	0.622207i	$-0.786236\pi$
$389$	−30.8805			−1.56571			−0.782853	+	0.622207i	$0.786236\pi$
$390$	−2.03639	−	1.72923i	−0.103117	−	0.0875630i
$391$	1.77113	+	3.06768i	0.0895698	+	0.155139i
$392$	−8.12759	+	0.527517i	−0.410505	+	0.0266436i
$393$	−5.69497	+	31.2238i	−0.287273	+	1.57503i
$394$	2.38987	+	4.13938i	0.120400	+	0.208539i
$395$	2.59268	+	4.49066i	0.130452	+	0.225949i
$396$	−21.5077	+	17.6206i	−1.08080	+	0.885467i
$397$	11.5595	−	20.0216i	0.580154	−	1.00486i	−0.415306	−	0.909682i	$-0.636326\pi$
$397$	11.5595	−	20.0216i	0.580154	−	1.00486i	0.995461	−	0.0951749i	$-0.0303410\pi$
$398$	−1.23552	+	2.13998i	−0.0619308	+	0.107267i
$399$	−14.5670	−	11.5788i	−0.729264	−	0.579665i
$400$	−1.73846	−	3.01111i	−0.0869232	−	0.150555i
$401$	−36.2568			−1.81058			−0.905288	−	0.424798i	$-0.860345\pi$
$401$	−36.2568			−1.81058			−0.905288	+	0.424798i	$0.860345\pi$
$402$	−0.699910	+	3.83740i	−0.0349084	+	0.191392i
$403$	−37.3381			−1.85994
$404$	0.854053	−	1.47926i	0.0424907	−	0.0735961i
$405$	−6.75654	−	5.94552i	−0.335735	−	0.295435i
$406$	3.62388	−	0.117480i	0.179850	−	0.00583041i
$407$	15.7697	−	27.3140i	0.781677	−	1.35390i
$408$	−6.83463	+	2.44222i	−0.338365	+	0.120908i
$409$	−0.275407	+	0.477019i	−0.0136180	+	0.0235871i	−0.872754	−	0.488160i	$-0.837668\pi$
$409$	−0.275407	+	0.477019i	−0.0136180	+	0.0235871i	0.859136	+	0.511747i	$0.171002\pi$
$410$	0.0887742	−	0.153761i	0.00438424	−	0.00759373i
$411$	1.50169	−	8.23329i	0.0740727	−	0.406118i
$412$	−0.854553	+	1.48013i	−0.0421008	+	0.0729207i
$413$	−9.36099	+	17.4998i	−0.460624	+	0.861108i
$414$	0.142247	+	0.866126i	0.00699108	+	0.0425678i
$415$	5.45891	−	9.45512i	0.267968	−	0.464133i
$416$	17.4292			0.854539
$417$	8.94069	−	3.19477i	0.437827	−	0.156449i
$418$	5.85647			0.286450
$419$	−10.4660	−	18.1277i	−0.511299	−	0.885596i	−0.999914	−	0.0130969i	$-0.995831\pi$
$419$	−10.4660	−	18.1277i	−0.511299	−	0.885596i	0.488615	−	0.872500i	$-0.337502\pi$
$420$	−6.85730	−	5.45062i	−0.334602	−	0.265963i
$421$	−1.98810	+	3.44350i	−0.0968942	+	0.167826i	−0.910398	−	0.413734i	$-0.864224\pi$
$421$	−1.98810	+	3.44350i	−0.0968942	+	0.167826i	0.813503	+	0.581560i	$0.197558\pi$
$422$	2.27140	−	3.93417i	0.110570	−	0.191513i
$423$	3.48004	+	21.1895i	0.169205	+	1.03027i
$424$	−5.57128	−	9.64974i	−0.270565	−	0.468633i
$425$	1.80070	+	3.11891i	0.0873469	+	0.151289i
$426$	−4.95231	+	1.76961i	−0.239940	+	0.0857378i
$427$	−20.9346	−	33.6895i	−1.01310	−	1.63035i
$428$	−7.18089	−	12.4377i	−0.347102	−	0.601198i
$429$	−41.0059	+	14.6526i	−1.97978	+	0.707435i
$430$	0.0336285			0.00162171
$431$	5.83449	+	10.1056i	0.281037	+	0.486771i	0.971640	−	0.236463i	$-0.0759882\pi$
$431$	5.83449	+	10.1056i	0.281037	+	0.486771i	−0.690603	+	0.723234i	$0.742655\pi$
$432$	18.0638	+	0.318463i	0.869097	+	0.0153221i
$433$	22.1128			1.06267			0.531337	−	0.847161i	$-0.321690\pi$
$433$	22.1128			1.06267			0.531337	+	0.847161i	$0.321690\pi$
$434$	5.66414	−	0.183621i	0.271887	−	0.00881408i
$435$	6.08250	+	5.16504i	0.291634	+	0.247644i
$436$	7.54232			0.361212
$437$	−1.99698	+	3.45887i	−0.0955285	+	0.165460i
$438$	1.31861	+	1.11972i	0.0630058	+	0.0535022i
$439$	14.2395	+	24.6636i	0.679616	+	1.17713i	0.975096	+	0.221781i	$0.0711870\pi$
$439$	14.2395	+	24.6636i	0.679616	+	1.17713i	−0.295480	+	0.955349i	$0.595480\pi$
$440$	5.64138			0.268942
$441$	−20.0867	−	6.12571i	−0.956510	−	0.291701i
$442$	−5.55486			−0.264218
$443$	0.999092	+	1.73048i	0.0474683	+	0.0822175i	0.888783	−	0.458328i	$-0.151551\pi$
$443$	0.999092	+	1.73048i	0.0474683	+	0.0822175i	−0.841315	+	0.540545i	$0.818218\pi$
$444$	−20.2810	+	7.24702i	−0.962495	+	0.343928i
$445$	7.64065	−	13.2340i	0.362201	−	0.627351i
$446$	1.56805			0.0742495
$447$	0.150859	−	0.827114i	0.00713539	−	0.0391212i
$448$	15.7445	−	0.510408i	0.743859	−	0.0241145i
$449$	35.6977			1.68468			0.842339	−	0.538948i	$-0.181178\pi$
$449$	35.6977			1.68468			0.842339	+	0.538948i	$0.181178\pi$
$450$	0.144623	+	0.880589i	0.00681758	+	0.0415113i
$451$	−1.44699	−	2.50625i	−0.0681359	−	0.118015i
$452$	32.0349			1.50680
$453$	−4.54236	+	24.9044i	−0.213419	+	1.17011i
$454$	2.30308	+	3.98904i	0.108089	+	0.187215i
$455$	−7.24080	−	11.6524i	−0.339454	−	0.546274i
$456$	−6.23782	−	5.29692i	−0.292113	−	0.248051i
$457$	19.3020	+	33.4321i	0.902911	+	1.56389i	0.823697	+	0.567030i	$0.191908\pi$
$457$	19.3020	+	33.4321i	0.902911	+	1.56389i	0.0792143	+	0.996858i	$0.474759\pi$
$458$	1.90905	+	3.30657i	0.0892040	+	0.154506i
$459$	−18.7105	−	0.329864i	−0.873333	−	0.0153967i
$460$	−0.940061	+	1.62823i	−0.0438306	+	0.0759168i
$461$	14.7256	−	25.5055i	0.685841	−	1.18791i	−0.287331	−	0.957831i	$-0.592768\pi$
$461$	14.7256	−	25.5055i	0.685841	−	1.18791i	0.973172	−	0.230079i	$-0.0738986\pi$
$462$	6.14848	−	2.42444i	0.286053	−	0.112795i
$463$	−15.4426	−	26.7474i	−0.717679	−	1.24306i	−0.961917	−	0.273341i	$-0.911871\pi$
$463$	−15.4426	−	26.7474i	−0.717679	−	1.24306i	0.244238	−	0.969715i	$-0.421462\pi$
$464$	−16.0183			−0.743633
$465$	9.50697	+	8.07296i	0.440875	+	0.374375i
$466$	1.18232			0.0547701
$467$	−3.92122	+	6.79175i	−0.181452	+	0.314285i	−0.942375	−	0.334557i	$-0.891413\pi$
$467$	−3.92122	+	6.79175i	−0.181452	+	0.314285i	0.760923	+	0.648842i	$0.224746\pi$
$468$	27.8204	+	10.4977i	1.28600	+	0.485255i
$469$	−9.44811	+	17.6627i	−0.436273	+	0.815585i
$470$	1.06458	−	1.84392i	0.0491056	−	0.0850535i
$471$	14.8690	+	12.6262i	0.685127	+	0.581785i
$472$	−4.36389	+	7.55848i	−0.200864	+	0.347907i
$473$	0.274066	−	0.474697i	0.0126016	−	0.0218266i
$474$	2.03644	+	1.72927i	0.0935366	+	0.0794278i
$475$	−2.03033	+	3.51663i	−0.0931578	+	0.161354i
$476$	−18.2042	+	0.590145i	−0.834387	+	0.0270493i
$477$	−4.65600	−	28.3498i	−0.213184	−	1.29805i
$478$	−3.78266	+	6.55175i	−0.173015	+	0.299670i
$479$	15.9737			0.729858			0.364929	−	0.931035i	$-0.381093\pi$
$479$	15.9737			0.729858			0.364929	+	0.931035i	$0.381093\pi$
$480$	−4.43781	−	3.76842i	−0.202557	−	0.172004i
$481$	−33.7299			−1.53795
$482$	0.646920	+	1.12050i	0.0294664	+	0.0510373i
$483$	−0.664659	+	4.45804i	−0.0302430	+	0.202848i
$484$	11.9547	−	20.7062i	0.543398	−	0.941192i
$485$	−6.85013	+	11.8648i	−0.311048	+	0.538752i
$486$	−4.30886	−	1.71325i	−0.195454	−	0.0777147i
$487$	−21.6824	−	37.5550i	−0.982523	−	1.70178i	−0.652465	−	0.757819i	$-0.726265\pi$
$487$	−21.6824	−	37.5550i	−0.982523	−	1.70178i	−0.330058	−	0.943961i	$-0.607068\pi$
$488$	−8.72157	−	15.1062i	−0.394807	−	0.683826i
$489$	18.0439	+	15.3222i	0.815971	+	0.692892i
$490$	1.15572	+	1.73205i	0.0522103	+	0.0782460i
$491$	−2.19367	−	3.79955i	−0.0989989	−	0.171471i	0.812272	−	0.583279i	$-0.198231\pi$
$491$	−2.19367	−	3.79955i	−0.0989989	−	0.171471i	−0.911271	+	0.411808i	$0.864897\pi$
$492$	−0.354588	+	1.94410i	−0.0159861	+	0.0876466i
$493$	16.5918			0.747258
$494$	−3.13161	−	5.42410i	−0.140898	−	0.244042i
$495$	13.6089	+	5.13516i	0.611676	+	0.230808i
$496$	−25.0367			−1.12418
$497$	−26.9917	+	0.875022i	−1.21074	+	0.0392501i
$498$	1.00932	−	5.53378i	0.0452286	−	0.247975i
$499$	−36.5941			−1.63818			−0.819088	−	0.573669i	$-0.805520\pi$
$499$	−36.5941			−1.63818			−0.819088	+	0.573669i	$0.805520\pi$
$500$	−0.955758	+	1.65542i	−0.0427428	+	0.0740327i
$501$	−4.67924	+	1.67203i	−0.209053	+	0.0747009i
$502$	−0.209048	−	0.362082i	−0.00933026	−	0.0161605i
$503$	35.9061			1.60097			0.800486	−	0.599352i	$-0.204575\pi$
$503$	35.9061			1.60097			0.800486	+	0.599352i	$0.204575\pi$
$504$	−8.74164	−	2.97872i	−0.389384	−	0.132683i
$505$	−0.893587			−0.0397641
$506$	−0.709281	−	1.22851i	−0.0315314	−	0.0546139i
$507$	18.3343	+	15.5688i	0.814256	+	0.691436i
$508$	2.42636	−	4.20258i	0.107652	−	0.186459i
$509$	1.04427			0.0462864			0.0231432	−	0.999732i	$-0.492633\pi$
$509$	1.04427			0.0462864			0.0231432	+	0.999732i	$0.492633\pi$
$510$	1.41437	+	1.20103i	0.0626294	+	0.0531826i
$511$	4.68859	+	7.54522i	0.207411	+	0.333781i
$512$	19.7780			0.874073
$513$	−10.2261	−	18.4561i	−0.451496	−	0.814855i
$514$	−1.21966	−	2.11251i	−0.0537968	−	0.0931788i
$515$	0.894109			0.0393992
$516$	−0.352470	+	0.125948i	−0.0155166	+	0.00554455i
$517$	−17.3523	−	30.0551i	−0.763155	−	1.32182i
$518$	5.11679	−	0.165877i	0.224819	−	0.00728821i
$519$	−8.40742	+	3.00422i	−0.369045	+	0.131871i
$520$	−3.01659	−	5.22489i	−0.132286	−	0.229127i
$521$	−10.5727	−	18.3125i	−0.463199	−	0.802284i	0.535919	−	0.844269i	$-0.319965\pi$
$521$	−10.5727	−	18.3125i	−0.463199	−	0.802284i	−0.999118	+	0.0419852i	$0.986632\pi$
$522$	3.84653	+	1.45144i	0.168358	+	0.0635276i
$523$	4.05630	−	7.02573i	0.177370	−	0.307214i	−0.763609	−	0.645679i	$-0.776574\pi$
$523$	4.05630	−	7.02573i	0.177370	−	0.307214i	0.940979	+	0.338465i	$0.109908\pi$
$524$	−17.5137	+	30.3347i	−0.765092	+	1.32518i
$525$	−0.675758	+	4.53248i	−0.0294925	+	0.197814i
$526$	−3.49041	−	6.04557i	−0.152189	−	0.263600i
$527$	25.9331			1.12966
$528$	−27.4961	+	9.82519i	−1.19662	+	0.427586i
$529$	−22.0326			−0.957938
$530$	−1.42433	+	2.46701i	−0.0618688	+	0.107160i
$531$	−17.4074	+	14.2613i	−0.755418	+	0.618890i
$532$	−10.8390	−	17.4430i	−0.469932	−	0.756248i
$533$	−1.54748	+	2.68032i	−0.0670289	+	0.116097i
$534$	1.41271	−	7.74543i	0.0611337	−	0.335178i
$535$	−3.75665	+	6.50670i	−0.162414	+	0.281309i
$536$	−4.40451	+	7.62883i	−0.190246	+	0.329515i
$537$	23.9929	−	8.57338i	1.03537	−	0.369969i
$538$	1.29553	−	2.24393i	0.0558544	−	0.0967426i
$539$	33.8684	−	2.19821i	1.45881	−	0.0946836i
$540$	−4.81387	−	8.68803i	−0.207156	−	0.373873i
$541$	18.3176	−	31.7270i	0.787534	−	1.36405i	−0.139939	−	0.990160i	$-0.544691\pi$
$541$	18.3176	−	31.7270i	0.787534	−	1.36405i	0.927473	−	0.373889i	$-0.121976\pi$
$542$	−4.33444			−0.186180
$543$	3.94366	−	21.6219i	0.169239	−	0.927885i
$544$	−12.1054			−0.519016
$545$	−1.97286	−	3.41710i	−0.0845082	−	0.146372i
$546$	−5.53320	−	4.39814i	−0.236799	−	0.188223i
$547$	8.98787	−	15.5674i	0.384293	−	0.665616i	−0.607377	−	0.794413i	$-0.707778\pi$
$547$	8.98787	−	15.5674i	0.384293	−	0.665616i	0.991671	+	0.128798i	$0.0411118\pi$
$548$	4.61814	−	7.99885i	0.197277	−	0.341694i
$549$	−7.28876	−	44.3803i	−0.311077	−	1.89410i
$550$	−0.721125	−	1.24902i	−0.0307489	−	0.0532586i
$551$	9.35380	+	16.2013i	0.398485	+	0.690196i
$552$	−0.355668	+	1.95002i	−0.0151382	+	0.0829983i
$553$	7.24095	+	11.6527i	0.307917	+	0.495522i
$554$	0.757437	+	1.31192i	0.0321804	+	0.0557381i
$555$	8.58827	+	7.29284i	0.364552	+	0.309564i
$556$	10.4781			0.444370
$557$	7.95551	+	13.7793i	0.337086	+	0.583850i	0.983883	−	0.178812i	$-0.0572254\pi$
$557$	7.95551	+	13.7793i	0.337086	+	0.583850i	−0.646797	+	0.762662i	$0.723892\pi$
$558$	6.01213	+	2.26860i	0.254514	+	0.0960374i
$559$	−0.586201			−0.0247937
$560$	−4.85526	−	7.81343i	−0.205172	−	0.330178i
$561$	28.4805	−	10.1769i	1.20245	−	0.429671i
$562$	2.67484			0.112831
$563$	1.24462	−	2.15574i	0.0524543	−	0.0908536i	−0.838606	−	0.544738i	$-0.816629\pi$
$563$	1.24462	−	2.15574i	0.0524543	−	0.0908536i	0.891060	+	0.453885i	$0.149962\pi$
$564$	−4.25224	+	23.3137i	−0.179051	+	0.981684i
$565$	−8.37945	−	14.5136i	−0.352526	−	0.610593i
$566$	−1.85737			−0.0780710
$567$	−18.3764	−	15.1429i	−0.771737	−	0.635942i
$568$	−11.8764			−0.498324
$569$	14.1804	+	24.5611i	0.594472	+	1.02966i	0.993621	+	0.112769i	$0.0359721\pi$
$569$	14.1804	+	24.5611i	0.594472	+	1.02966i	−0.399150	+	0.916886i	$0.630695\pi$
$570$	−0.375394	+	2.05817i	−0.0157235	+	0.0862073i
$571$	11.8121	−	20.4592i	0.494321	−	0.856189i	−0.505658	−	0.862734i	$-0.668750\pi$
$571$	11.8121	−	20.4592i	0.494321	−	0.856189i	0.999979	+	0.00654532i	$0.00208346\pi$
$572$	−48.0571			−2.00937
$573$	−14.5699	+	5.20627i	−0.608667	+	0.217495i
$574$	0.221570	−	0.414211i	0.00924815	−	0.0172888i
$575$	0.983576			0.0410179
$576$	16.7118	+	6.30599i	0.696326	+	0.262749i
$577$	5.28480	+	9.15355i	0.220009	+	0.381067i	0.954810	−	0.297215i	$-0.0960579\pi$
$577$	5.28480	+	9.15355i	0.220009	+	0.381067i	−0.734801	+	0.678282i	$0.762725\pi$
$578$	−1.19874			−0.0498609
$579$	2.24978	+	1.91043i	0.0934978	+	0.0793948i
$580$	4.40322	+	7.62659i	0.182834	+	0.316677i
$581$	13.6248	−	25.4707i	0.565252	−	1.05670i
$582$	−1.26654	+	6.94407i	−0.0524999	+	0.287841i
$583$	23.2160	+	40.2113i	0.961508	+	1.66538i
$584$	1.95332	+	3.38324i	0.0808288	+	0.140000i
$585$	−2.52101	−	15.3501i	−0.104231	−	0.634650i
$586$	4.29840	−	7.44504i	0.177565	−	0.307552i
$587$	1.63865	−	2.83822i	0.0676342	−	0.117146i	−0.830225	−	0.557428i	$-0.811788\pi$
$587$	1.63865	−	2.83822i	0.0676342	−	0.117146i	0.897859	+	0.440282i	$0.145122\pi$
$588$	−18.6004	−	13.8256i	−0.767069	−	0.570156i
$589$	14.6200	+	25.3226i	0.602407	+	1.04340i
$590$	2.23130			0.0918614
$591$	−4.99382	+	27.3796i	−0.205418	+	1.12625i
$592$	−22.6173			−0.929566
$593$	4.54630	−	7.87442i	0.186694	−	0.323364i	−0.757452	−	0.652891i	$-0.773556\pi$
$593$	4.54630	−	7.87442i	0.186694	−	0.323364i	0.944146	+	0.329527i	$0.106889\pi$
$594$	7.49298	+	0.132100i	0.307441	+	0.00542014i
$595$	5.02908	+	8.09316i	0.206172	+	0.331787i
$596$	0.463937	−	0.803563i	0.0190036	−	0.0329152i
$597$	−13.5492	+	4.84153i	−0.554532	+	0.198151i
$598$	−0.758541	+	1.31383i	−0.0310191	+	0.0537266i
$599$	3.58075	−	6.20204i	0.146305	−	0.253409i	−0.783554	−	0.621324i	$-0.786595\pi$
$599$	3.58075	−	6.20204i	0.146305	−	0.253409i	0.929859	+	0.367915i	$0.119928\pi$
$600$	−0.361607	+	1.98258i	−0.0147625	+	0.0809385i
$601$	3.47029	−	6.01072i	0.141556	−	0.245182i	−0.786527	−	0.617556i	$-0.788123\pi$
$601$	3.47029	−	6.01072i	0.141556	−	0.245182i	0.928083	+	0.372374i	$0.121456\pi$
$602$	0.0889260	−	0.00288282i	0.00362435	−	0.000117495i
$603$	−17.5694	+	14.3941i	−0.715483	+	0.586172i
$604$	−13.9691	+	24.1952i	−0.568396	+	0.984490i
$605$	−12.5081			−0.508528
$606$	−0.433546	+	0.154919i	−0.0176116	+	0.00629315i
$607$	−1.52225			−0.0617864			−0.0308932	−	0.999523i	$-0.509835\pi$
$607$	−1.52225			−0.0617864			−0.0308932	+	0.999523i	$0.509835\pi$
$608$	−6.82455	−	11.8205i	−0.276772	−	0.479383i
$609$	16.5271	+	13.1368i	0.669713	+	0.532330i
$610$	−2.22972	+	3.86198i	−0.0902786	+	0.156367i
$611$	−18.5575	+	32.1425i	−0.750756	+	1.30035i
$612$	−19.3226	−	7.29113i	−0.781069	−	0.294726i
$613$	−4.69889	−	8.13872i	−0.189786	−	0.328720i	0.755393	−	0.655273i	$-0.227446\pi$
$613$	−4.69889	−	8.13872i	−0.189786	−	0.328720i	−0.945179	+	0.326553i	$0.894113\pi$
$614$	−3.62686	−	6.28190i	−0.146368	−	0.253517i
$615$	0.973536	−	0.347874i	0.0392568	−	0.0140276i
$616$	14.9179	−	0.483609i	0.601057	−	0.0194852i
$617$	13.6316	+	23.6106i	0.548786	+	0.950526i	0.998358	+	0.0572817i	$0.0182433\pi$
$617$	13.6316	+	23.6106i	0.548786	+	0.950526i	−0.449572	+	0.893244i	$0.648423\pi$
$618$	0.433799	−	0.155009i	0.0174500	−	0.00623539i
$619$	−2.92756			−0.117669			−0.0588343	−	0.998268i	$-0.518738\pi$
$619$	−2.92756			−0.117669			−0.0588343	+	0.998268i	$0.518738\pi$
$620$	6.88224	+	11.9204i	0.276397	+	0.478734i
$621$	−2.63303	+	4.38036i	−0.105660	+	0.175778i
$622$	5.26379			0.211059
$623$	19.0701	−	35.6505i	0.764029	−	1.42831i
$624$	23.8027	+	20.2124i	0.952871	+	0.809142i
$625$	1.00000			0.0400000
$626$	−0.0774985	+	0.134231i	−0.00309746	+	0.00536497i
$627$	25.9935	+	22.0727i	1.03808	+	0.881500i
$628$	10.7639	+	18.6436i	0.429526	+	0.743961i
$629$	23.4270			0.934097
$630$	0.457923	+	2.31620i	0.0182441	+	0.0922795i
$631$	−17.6173			−0.701332			−0.350666	−	0.936501i	$-0.614045\pi$
$631$	−17.6173			−0.701332			−0.350666	+	0.936501i	$0.614045\pi$
$632$	3.01665	+	5.22500i	0.119996	+	0.207839i
$633$	24.9091	−	8.90077i	0.990049	−	0.353774i
$634$	2.80824	−	4.86401i	0.111529	−	0.193174i
$635$	−2.53868			−0.100744
$636$	5.68914	−	31.1918i	0.225589	−	1.23684i
$637$	−20.1462	−	30.1925i	−0.798222	−	1.19627i
$638$	−6.64450			−0.263058
$639$	−28.6500	−	10.8107i	−1.13338	−	0.427665i
$640$	−4.24685	−	7.35576i	−0.167871	−	0.290762i
$641$	25.6279			1.01224			0.506121	−	0.862463i	$-0.331079\pi$
$641$	25.6279			1.01224			0.506121	+	0.862463i	$0.331079\pi$
$642$	−0.694579	+	3.80817i	−0.0274129	+	0.150296i
$643$	10.0950	+	17.4850i	0.398108	+	0.689543i	0.993492	−	0.113898i	$-0.0363337\pi$
$643$	10.0950	+	17.4850i	0.398108	+	0.689543i	−0.595385	+	0.803441i	$0.703000\pi$
$644$	−2.34628	+	4.38622i	−0.0924564	+	0.172841i
$645$	0.149258	+	0.126744i	0.00587702	+	0.00499055i
$646$	2.17505	+	3.76730i	0.0855762	+	0.148222i
$647$	−6.26172	−	10.8456i	−0.246174	−	0.426385i	0.716287	−	0.697805i	$-0.245840\pi$
$647$	−6.26172	−	10.8456i	−0.246174	−	0.426385i	−0.962461	+	0.271420i	$0.912507\pi$
$648$	−7.86141	−	6.91777i	−0.308825	−	0.271756i
$649$	18.1847	−	31.4969i	0.713813	−	1.23636i
$650$	−0.771208	+	1.33577i	−0.0302493	+	0.0523933i
$651$	25.8319	+	20.5329i	1.01243	+	0.804746i
$652$	13.0622	+	22.6244i	0.511556	+	0.886041i
$653$	−26.2813			−1.02847			−0.514234	−	0.857650i	$-0.671924\pi$
$653$	−26.2813			−1.02847			−0.514234	+	0.857650i	$0.671924\pi$
$654$	−1.54960	−	1.31586i	−0.0605940	−	0.0514542i
$655$	18.3245			0.715996
$656$	−1.03765	+	1.79726i	−0.0405135	+	0.0701714i
$657$	1.63242	+	9.93957i	0.0636866	+	0.387780i
$658$	2.65708	−	4.96724i	0.103584	−	0.193643i
$659$	−9.31059	+	16.1264i	−0.362689	+	0.628196i	−0.988402	−	0.151857i	$-0.951475\pi$
$659$	−9.31059	+	16.1264i	−0.362689	+	0.628196i	0.625713	+	0.780053i	$0.284808\pi$
$660$	12.2362	+	10.3905i	0.476294	+	0.404451i
$661$	−6.41289	+	11.1074i	−0.249432	+	0.432030i	−0.963368	−	0.268181i	$-0.913577\pi$
$661$	−6.41289	+	11.1074i	−0.249432	+	0.432030i	0.713936	+	0.700211i	$0.246911\pi$
$662$	−3.90844	+	6.76962i	−0.151906	+	0.263109i
$663$	−24.6549	−	20.9360i	−0.957515	−	0.813086i
$664$	6.35159	−	11.0013i	0.246490	−	0.426933i
$665$	−5.06746	+	9.47329i	−0.196507	+	0.367358i
$666$	5.43115	+	2.04937i	0.210453	+	0.0794116i
$667$	2.26569	−	3.92428i	0.0877277	−	0.151949i
$668$	−5.48386			−0.212177
$669$	6.95969	+	5.90991i	0.269077	+	0.228490i
$670$	2.25207			0.0870051
$671$	36.3436	+	62.9489i	1.40303	+	2.43011i
$672$	−12.0582	−	9.58464i	−0.465156	−	0.369735i
$673$	−2.96152	+	5.12950i	−0.114158	+	0.197728i	−0.917443	−	0.397867i	$-0.869750\pi$
$673$	−2.96152	+	5.12950i	−0.114158	+	0.197728i	0.803285	+	0.595595i	$0.203084\pi$
$674$	3.56527	−	6.17523i	0.137329	−	0.237861i
$675$	−2.67699	+	4.45350i	−0.103038	+	0.171415i
$676$	13.2725	+	22.9886i	0.510481	+	0.884178i
$677$	17.9477	+	31.0864i	0.689787	+	1.19475i	0.971907	+	0.235367i	$0.0756292\pi$
$677$	17.9477	+	31.0864i	0.689787	+	1.19475i	−0.282120	+	0.959379i	$0.591037\pi$
$678$	−6.58169	−	5.58892i	−0.252768	−	0.214641i
$679$	−17.0971	+	31.9620i	−0.656127	+	1.22659i
$680$	2.09517	+	3.62893i	0.0803459	+	0.139163i
$681$	−4.81246	+	26.3853i	−0.184414	+	1.01109i
$682$	−10.3854			−0.397676
$683$	−18.6509	−	32.3042i	−0.713655	−	1.23609i	−0.963476	−	0.267795i	$-0.913705\pi$
$683$	−18.6509	−	32.3042i	−0.713655	−	1.23609i	0.249821	−	0.968292i	$-0.419628\pi$
$684$	−3.77380	−	22.9782i	−0.144295	−	0.878593i
$685$	−4.83191			−0.184618
$686$	3.20464	+	4.48109i	0.122354	+	0.171089i
$687$	−3.98911	+	21.8711i	−0.152194	+	0.834433i
$688$	−0.393072			−0.0149857
$689$	24.8284	−	43.0040i	0.945886	−	1.63832i
$690$	0.477206	−	0.170520i	0.0181669	−	0.00649158i
$691$	21.0657	+	36.4869i	0.801379	+	1.38803i	0.918709	+	0.394936i	$0.129233\pi$
$691$	21.0657	+	36.4869i	0.801379	+	1.38803i	−0.117330	+	0.993093i	$0.537433\pi$
$692$	−9.85313			−0.374560
$693$	36.4272	+	12.4126i	1.38375	+	0.471515i
$694$	−2.19074			−0.0831594
$695$	−2.74078	−	4.74717i	−0.103964	−	0.180070i
$696$	7.07716	+	6.00966i	0.268259	+	0.227795i
$697$	1.07480	−	1.86161i	0.0407109	−	0.0705134i
$698$	−5.20315			−0.196942
$699$	5.24766	+	4.45612i	0.198485	+	0.168546i
$700$	−2.38546	+	4.45947i	−0.0901619	+	0.168552i
$701$	−21.3429			−0.806112			−0.403056	−	0.915175i	$-0.632052\pi$
$701$	−21.3429			−0.806112			−0.403056	+	0.915175i	$0.632052\pi$
$702$	−3.88434	−	7.01043i	−0.146605	−	0.264592i
$703$	13.2072	+	22.8756i	0.498119	+	0.862768i
$704$	−28.8681			−1.08801
$705$	11.6747	−	4.17172i	0.439695	−	0.157116i
$706$	−4.53799	−	7.86003i	−0.170789	−	0.295816i
$707$	−2.36297	+	0.0766030i	−0.0888685	+	0.00288095i
$708$	−23.3869	+	8.35684i	−0.878933	+	0.314069i
$709$	−1.86432	−	3.22909i	−0.0700159	−	0.121271i	0.828892	−	0.559408i	$-0.188972\pi$
$709$	−1.86432	−	3.22909i	−0.0700159	−	0.121271i	−0.898908	+	0.438137i	$0.855638\pi$
$710$	1.51814	+	2.62949i	0.0569747	+	0.0986830i
$711$	2.52107	+	15.3504i	0.0945474	+	0.575687i
$712$	8.89010	−	15.3981i	0.333170	−	0.577068i
$713$	3.54127	−	6.13367i	0.132622	−	0.229708i
$714$	3.84307	+	3.05472i	0.143823	+	0.114320i
$715$	12.5704	+	21.7726i	0.470106	+	0.814248i
$716$	28.1186			1.05084
$717$	−41.4823	+	14.8229i	−1.54918	+	0.553570i
$718$	4.70101			0.175440
$719$	−8.98333	+	15.5596i	−0.335022	+	0.580275i	−0.983489	−	0.180968i	$-0.942077\pi$
$719$	−8.98333	+	15.5596i	−0.335022	+	0.580275i	0.648467	+	0.761243i	$0.275410\pi$
$720$	−1.69044	−	10.2929i	−0.0629991	−	0.383593i
$721$	2.36435	−	0.0766478i	0.0880530	−	0.00285451i
$722$	0.373477	−	0.646881i	0.0138994	−	0.0240744i
$723$	−1.35179	+	7.41146i	−0.0502737	+	0.275635i
$724$	12.1280	−	21.0062i	0.450732	−	0.780690i
$725$	2.30352	−	3.98981i	0.0855506	−	0.148178i
$726$	−6.06863	+	2.16850i	−0.225228	+	0.0804806i
$727$	3.76738	−	6.52529i	0.139724	−	0.242009i	−0.787668	−	0.616100i	$-0.788712\pi$
$727$	3.76738	−	6.52529i	0.139724	−	0.242009i	0.927392	+	0.374091i	$0.122045\pi$
$728$	−8.42487	−	13.5579i	−0.312246	−	0.502489i
$729$	−12.6674	−	23.8440i	−0.469163	−	0.883112i
$730$	0.499376	−	0.864944i	0.0184827	−	0.0320130i
$731$	0.407145			0.0150588
$732$	8.90608	−	48.8293i	0.329178	−	1.80478i
$733$	−7.68730			−0.283937			−0.141968	−	0.989871i	$-0.545343\pi$
$733$	−7.68730			−0.283937			−0.141968	+	0.989871i	$0.545343\pi$
$734$	−3.68725	−	6.38650i	−0.136099	−	0.235730i
$735$	−1.39840	+	12.0434i	−0.0515808	+	0.444229i
$736$	−1.65305	+	2.86317i	−0.0609322	+	0.105538i
$737$	18.3540	−	31.7900i	0.676077	−	1.17100i
$738$	0.412025	−	0.337559i	0.0151669	−	0.0124257i
$739$	14.7136	+	25.4848i	0.541250	+	0.937472i	0.998833	+	0.0483049i	$0.0153819\pi$
$739$	14.7136	+	25.4848i	0.541250	+	0.937472i	−0.457583	+	0.889167i	$0.651285\pi$
$740$	6.21718	+	10.7685i	0.228548	+	0.395857i
$741$	6.54375	−	35.8774i	0.240390	−	1.31799i
$742$	−3.55495	+	6.64576i	−0.130506	+	0.243973i
$743$	5.61029	+	9.71730i	0.205821	+	0.356493i	0.950394	−	0.311048i	$-0.100680\pi$
$743$	5.61029	+	9.71730i	0.205821	+	0.356493i	−0.744573	+	0.667541i	$0.767347\pi$
$744$	11.0616	+	9.39311i	0.405539	+	0.344368i
$745$	−0.485413			−0.0177841
$746$	2.57754	+	4.46443i	0.0943704	+	0.163454i
$747$	25.3363	−	20.7572i	0.927007	−	0.759467i
$748$	33.3779			1.22042
$749$	−9.37615	+	17.5281i	−0.342597	+	0.640464i
$750$	0.485175	−	0.173367i	0.0177161	−	0.00633048i
$751$	−38.0518			−1.38853			−0.694264	−	0.719720i	$-0.744270\pi$
$751$	−38.0518			−1.38853			−0.694264	+	0.719720i	$0.744270\pi$
$752$	−12.4436	+	21.5529i	−0.453770	+	0.785953i
$753$	0.436822	−	2.39496i	0.0159187	−	0.0872773i
$754$	3.55298	+	6.15395i	0.129392	+	0.224114i
$755$	14.6157			0.531922
$756$	−13.4744	−	22.5616i	−0.490059	−	0.820558i
$757$	1.17327			0.0426431			0.0213215	−	0.999773i	$-0.493213\pi$
$757$	1.17327			0.0426431			0.0213215	+	0.999773i	$0.493213\pi$
$758$	1.53574	+	2.65998i	0.0557805	+	0.0966147i
$759$	1.48210	−	8.12590i	0.0537968	−	0.294951i
$760$	−2.36234	+	4.09169i	−0.0856911	+	0.148421i
$761$	47.1040			1.70752			0.853760	−	0.520667i	$-0.174317\pi$
$761$	47.1040			1.70752			0.853760	+	0.520667i	$0.174317\pi$
$762$	−1.23170	+	0.440124i	−0.0446198	+	0.0159440i
$763$	−5.50990	−	8.86692i	−0.199472	−	0.321004i
$764$	−17.0753			−0.617763
$765$	1.75096	+	10.6614i	0.0633062	+	0.385463i
$766$	−0.867468	−	1.50250i	−0.0313429	−	0.0542875i
$767$	−38.8954			−1.40443
$768$	12.3860	+	10.5177i	0.446940	+	0.379525i
$769$	−1.40677	−	2.43659i	−0.0507293	−	0.0878657i	0.839546	−	0.543289i	$-0.182821\pi$
$769$	−1.40677	−	2.43659i	−0.0507293	−	0.0878657i	−0.890275	+	0.455423i	$0.849488\pi$
$770$	−2.01399	−	3.24105i	−0.0725791	−	0.116799i
$771$	2.54857	−	13.9731i	0.0917846	−	0.503227i
$772$	1.62865	+	2.82091i	0.0586165	+	0.101527i
$773$	−8.08332	−	14.0007i	−0.290737	−	0.503571i	0.683247	−	0.730187i	$-0.260567\pi$
$773$	−8.08332	−	14.0007i	−0.290737	−	0.503571i	−0.973984	+	0.226616i	$0.927234\pi$
$774$	0.0943894	+	0.0356166i	0.00339276	+	0.00128021i
$775$	3.60041	−	6.23609i	0.129330	−	0.224007i
$776$	−7.97031	+	13.8050i	−0.286117	+	0.495570i
$777$	23.3357	+	18.5487i	0.837163	+	0.665430i
$778$	4.59289	+	7.95512i	0.164663	+	0.285205i
$779$	2.42371			0.0868386
$780$	3.08041	−	16.8889i	0.110296	−	0.604721i
$781$	49.4902			1.77090
$782$	0.526843	−	0.912519i	0.0188399	−	0.0326316i
$783$	11.6021	+	20.9394i	0.414627	+	0.748315i
$784$	−13.5089	−	20.2453i	−0.482459	−	0.723047i
$785$	5.63107	−	9.75331i	0.200982	−	0.348110i
$786$	8.89056	−	3.17686i	0.317116	−	0.113315i
$787$	−14.1398	+	24.4908i	−0.504029	+	0.873003i	0.495960	+	0.868345i	$0.334816\pi$
$787$	−14.1398	+	24.4908i	−0.504029	+	0.873003i	−0.999989	+	0.00465821i	$0.998517\pi$
$788$	−15.3575	+	26.6000i	−0.547089	+	0.947586i
$789$	7.29350	−	39.9880i	0.259655	−	1.42361i
$790$	0.771224	−	1.33580i	0.0274389	−	0.0475256i
$791$	−23.4025	−	37.6610i	−0.832097	−	1.33907i
$792$	15.8344	+	5.97489i	0.562650	+	0.212309i
$793$	38.8677	−	67.3208i	1.38023	−	2.39063i
$794$	−6.87701			−0.244056
$795$	−15.6198	+	5.58142i	−0.553977	+	0.197952i
$796$	−15.8791			−0.562819
$797$	−23.6226	−	40.9155i	−0.836754	−	1.44930i	−0.892594	−	0.450860i	$-0.851117\pi$
$797$	−23.6226	−	40.9155i	−0.836754	−	1.44930i	0.0558406	−	0.998440i	$-0.482216\pi$
$798$	−0.816241	+	5.47473i	−0.0288946	+	0.193803i
$799$	12.8891	−	22.3245i	0.455982	−	0.789784i
$800$	−1.68065	+	2.91098i	−0.0594201	+	0.102919i
$801$	35.4623	−	29.0531i	1.25300	−	1.02654i
$802$	5.39250	+	9.34009i	0.190416	+	0.329810i
$803$	−8.13964	−	14.0983i	−0.287242	−	0.497517i
$804$	−23.6046	+	8.43461i	−0.832468	+	0.297466i
$805$	2.60093	−	0.0843173i	0.0916708	−	0.00297180i
$806$	5.55333	+	9.61864i	0.195608	+	0.338802i
$807$	14.2074	−	5.07672i	0.500123	−	0.178709i
$808$	−1.03971			−0.0365769
$809$	10.3977	+	18.0093i	0.365563	+	0.633174i	0.988866	−	0.148806i	$-0.0475431\pi$
$809$	10.3977	+	18.0093i	0.365563	+	0.633174i	−0.623303	+	0.781980i	$0.714210\pi$
$810$	−0.526717	+	2.62483i	−0.0185070	+	0.0922271i
$811$	−39.9166			−1.40166			−0.700831	−	0.713327i	$-0.747187\pi$
$811$	−39.9166			−1.40166			−0.700831	+	0.713327i	$0.747187\pi$
$812$	12.2975	+	19.7900i	0.431557	+	0.694493i
$813$	−19.2381	−	16.3363i	−0.674710	−	0.572938i
$814$	−9.38179			−0.328831
$815$	6.83343	−	11.8358i	0.239365	−	0.414592i
$816$	−16.5321	−	14.0384i	−0.578739	−	0.491444i
$817$	0.229532	+	0.397561i	0.00803030	+	0.0139089i
$818$	0.163846			0.00572875
$819$	−7.98237	−	40.3752i	−0.278926	−	1.41082i
$820$	1.14094			0.0398434
$821$	11.6699	+	20.2129i	0.407284	+	0.705436i	0.994584	−	0.103933i	$-0.0331427\pi$
$821$	11.6699	+	20.2129i	0.407284	+	0.705436i	−0.587301	+	0.809369i	$0.699809\pi$
$822$	−2.34432	+	0.837696i	−0.0817675	+	0.0292180i
$823$	2.70461	−	4.68453i	0.0942769	−	0.163292i	−0.815030	−	0.579419i	$-0.803279\pi$
$823$	2.70461	−	4.68453i	0.0942769	−	0.163292i	0.909307	+	0.416127i	$0.136613\pi$
$824$	1.04032			0.0362413
$825$	1.50685	−	8.26159i	0.0524617	−	0.287631i
$826$	5.90038	−	0.191279i	0.205300	−	0.00665546i
$827$	−30.6689			−1.06646			−0.533231	−	0.845970i	$-0.679022\pi$
$827$	−30.6689			−1.06646			−0.533231	+	0.845970i	$0.679022\pi$
$828$	−4.36308	+	3.57453i	−0.151627	+	0.124223i
$829$	−11.9890	−	20.7655i	−0.416394	−	0.721216i	0.579179	−	0.815200i	$-0.303373\pi$
$829$	−11.9890	−	20.7655i	−0.416394	−	0.721216i	−0.995574	+	0.0939839i	$0.970040\pi$
$830$	−3.24764			−0.112727
$831$	−1.58273	+	8.67760i	−0.0549041	+	0.301023i
$832$	15.4365	+	26.7368i	0.535164	+	0.926931i
$833$	13.9925	+	20.9701i	0.484811	+	0.726572i
$834$	−2.15276	−	1.82804i	−0.0745440	−	0.0633000i
$835$	1.43443	+	2.48450i	0.0496404	+	0.0859797i
$836$	18.8171	+	32.5922i	0.650804	+	1.12722i
$837$	18.1342	+	32.7284i	0.626809	+	1.13126i
$838$	−3.11325	+	5.39230i	−0.107545	+	0.186274i
$839$	9.10414	−	15.7688i	0.314310	−	0.544400i	−0.664981	−	0.746860i	$-0.731560\pi$
$839$	9.10414	−	15.7688i	0.314310	−	0.544400i	0.979291	+	0.202460i	$0.0648936\pi$
$840$	−0.786262	+	5.27366i	−0.0271286	+	0.181959i
$841$	3.88759	+	6.73351i	0.134055	+	0.232190i
$842$	1.18277			0.0407609
$843$	11.8721	+	10.0813i	0.408897	+	0.347220i
$844$	29.1924			1.00484
$845$	6.94344	−	12.0264i	0.238862	−	0.413720i
$846$	4.94103	−	4.04803i	0.169876	−	0.139174i
$847$	−33.0760	+	1.07226i	−1.13651	+	0.0368434i
$848$	16.6485	−	28.8360i	0.571710	−	0.990232i
$849$	−8.24379	−	7.00032i	−0.282926	−	0.240250i
$850$	0.535640	−	0.927756i	0.0183723	−	0.0318218i
$851$	3.19907	−	5.54094i	0.109663	−	0.189941i
$852$	−25.7601	−	21.8746i	−0.882528	−	0.749410i
$853$	−5.99343	+	10.3809i	−0.205211	+	0.355436i	−0.950200	−	0.311641i	$-0.899121\pi$
$853$	−5.99343	+	10.3809i	−0.205211	+	0.355436i	0.744989	+	0.667077i	$0.232455\pi$
$854$	−5.56511	+	10.4036i	−0.190434	+	0.356005i
$855$	−9.42330	+	7.72021i	−0.322270	+	0.264025i
$856$	−4.37096	+	7.57072i	−0.149396	+	0.258762i
$857$	−48.9711			−1.67282			−0.836411	−	0.548102i	$-0.815350\pi$
$857$	−48.9711			−1.67282			−0.836411	+	0.548102i	$0.815350\pi$
$858$	9.87349	+	8.38420i	0.337076	+	0.286232i
$859$	2.49908			0.0852674			0.0426337	−	0.999091i	$-0.486425\pi$
$859$	2.49908			0.0852674			0.0426337	+	0.999091i	$0.486425\pi$
$860$	0.108050	+	0.187148i	0.00368447	+	0.00638170i
$861$	2.54456	−	1.00336i	0.0867184	−	0.0341944i
$862$	1.73554	−	3.00604i	0.0591126	−	0.102386i
$863$	8.69174	−	15.0545i	0.295870	−	0.512462i	−0.679317	−	0.733845i	$-0.737724\pi$
$863$	8.69174	−	15.0545i	0.295870	−	0.512462i	0.975187	+	0.221383i	$0.0710571\pi$
$864$	−8.46495	−	15.2775i	−0.287983	−	0.519750i
$865$	2.57731	+	4.46403i	0.0876311	+	0.151781i
$866$	−3.28886	−	5.69647i	−0.111760	−	0.193574i
$867$	−5.32051	−	4.51797i	−0.180694	−	0.153438i
$868$	19.2210	+	30.9318i	0.652404	+	1.04990i
$869$	−12.5707	−	21.7730i	−0.426431	−	0.738599i
$870$	0.425906	−	2.33511i	0.0144396	−	0.0791677i
$871$	−39.2574			−1.33018
$872$	−2.29548	−	3.97589i	−0.0777347	−	0.134641i
$873$	−31.7933	+	26.0472i	−1.07604	+	0.881566i
$874$	1.18805			0.0401864
$875$	2.64436	−	0.0857253i	0.0893958	−	0.00289804i
$876$	−1.99464	+	10.9360i	−0.0673926	+	0.369493i
$877$	−51.8273			−1.75008			−0.875042	−	0.484048i	$-0.839166\pi$
$877$	−51.8273			−1.75008			−0.875042	+	0.484048i	$0.839166\pi$
$878$	4.23572	−	7.33648i	0.142949	−	0.247594i
$879$	47.1381	−	16.8438i	1.58993	−	0.568129i
$880$	8.42897	+	14.5994i	0.284141	+	0.492146i
$881$	−4.21967			−0.142164			−0.0710821	−	0.997470i	$-0.522645\pi$
$881$	−4.21967			−0.142164			−0.0710821	+	0.997470i	$0.522645\pi$
$882$	1.40947	+	6.08561i	0.0474594	+	0.204913i
$883$	14.3770			0.483824			0.241912	−	0.970298i	$-0.422225\pi$
$883$	14.3770			0.483824			0.241912	+	0.970298i	$0.422225\pi$
$884$	−17.8480	−	30.9137i	−0.600294	−	1.03974i
$885$	9.90349	+	8.40967i	0.332902	+	0.282688i
$886$	0.297192	−	0.514751i	0.00998435	−	0.0172934i
$887$	−24.7465			−0.830907			−0.415453	−	0.909614i	$-0.636377\pi$
$887$	−24.7465			−0.830907			−0.415453	+	0.909614i	$0.636377\pi$
$888$	9.99268	+	8.48541i	0.335332	+	0.284752i
$889$	−6.71318	+	0.217629i	−0.225153	+	0.00729904i
$890$	−4.54560			−0.152369
$891$	32.7592	+	28.8270i	1.09747	+	0.965740i
$892$	5.03822	+	8.72646i	0.168692	+	0.292184i
$893$	29.0653			0.972634
$894$	−0.235510	+	0.0841547i	−0.00787663	+	0.00281455i
$895$	−7.35505	−	12.7393i	−0.245852	−	0.425829i
$896$	−11.8608	−	19.0872i	−0.396241	−	0.637660i
$897$	−8.31850	+	2.97245i	−0.277746	+	0.0992471i
$898$	−5.30935	−	9.19607i	−0.177175	−	0.306877i
$899$	−16.5872	−	28.7299i	−0.553215	−	0.958196i
$900$	−4.43593	+	3.63422i	−0.147864	+	0.121141i
$901$	−17.2445	+	29.8683i	−0.574497	+	0.995058i
$902$	−0.430423	+	0.745515i	−0.0143315	+	0.0248229i
$903$	0.405557	+	0.322362i	0.0134961	+	0.0107275i
$904$	−9.74971	−	16.8870i	−0.324271	−	0.561653i
$905$	−12.6894			−0.421808
$906$	7.09119	−	2.53389i	0.235589	−	0.0841830i
$907$	−27.5446			−0.914604			−0.457302	−	0.889311i	$-0.651184\pi$
$907$	−27.5446			−0.914604			−0.457302	+	0.889311i	$0.651184\pi$
$908$	−14.7998	+	25.6340i	−0.491148	+	0.850693i
$909$	−2.50814	−	0.946414i	−0.0831898	−	0.0313906i
$910$	−1.92484	+	3.59837i	−0.0638079	+	0.119285i
$911$	2.35903	−	4.08597i	0.0781583	−	0.135374i	−0.824297	−	0.566158i	$-0.808429\pi$
$911$	2.35903	−	4.08597i	0.0781583	−	0.135374i	0.902455	+	0.430783i	$0.141763\pi$
$912$	4.38785	−	24.0573i	0.145296	−	0.796615i
$913$	−26.4676	+	45.8433i	−0.875951	+	1.51719i
$914$	5.74162	−	9.94478i	0.189916	−	0.328944i
$915$	−24.4520	+	8.73745i	−0.808360	+	0.288851i
$916$	−12.2677	+	21.2483i	−0.405337	+	0.702064i
$917$	48.4565	−	1.57087i	1.60017	−	0.0518747i
$918$	2.69786	+	4.86907i	0.0890426	+	0.160703i
$919$	−6.36798	+	11.0297i	−0.210060	+	0.363835i	−0.951733	−	0.306927i	$-0.900699\pi$
$919$	−6.36798	+	11.0297i	−0.210060	+	0.363835i	0.741673	+	0.670762i	$0.234033\pi$
$920$	1.14442			0.0377303
$921$	7.57860	−	41.5512i	0.249724	−	1.36916i
$922$	−8.76062			−0.288516
$923$	−26.4637	−	45.8364i	−0.871062	−	1.50872i
$924$	33.2477	+	26.4274i	1.09377	+	0.869398i
$925$	3.25248	−	5.63347i	0.106941	−	0.185227i
$926$	−4.59359	+	7.95632i	−0.150955	+	0.261461i
$927$	2.50961	+	0.946968i	0.0824264	+	0.0311025i
$928$	7.74284	+	13.4110i	0.254171	+	0.440237i
$929$	−17.5245	−	30.3532i	−0.574959	−	0.995858i	−0.996046	−	0.0888377i	$-0.971685\pi$
$929$	−17.5245	−	30.3532i	−0.574959	−	0.995858i	0.421087	−	0.907020i	$-0.361649\pi$
$930$	0.665692	−	3.64979i	0.0218289	−	0.119681i
$931$	−12.5881	+	25.4852i	−0.412558	+	0.835244i
$932$	3.79886	+	6.57982i	0.124436	+	0.215529i
$933$	23.3629	+	19.8389i	0.764868	+	0.649498i
$934$	2.33283			0.0763324
$935$	−8.73074	−	15.1221i	−0.285526	−	0.494545i
$936$	−2.93327	−	17.8603i	−0.0958768	−	0.583782i
$937$	19.4636			0.635848			0.317924	−	0.948116i	$-0.397014\pi$
$937$	19.4636			0.635848			0.317924	+	0.948116i	$0.397014\pi$
$938$	5.95529	−	0.193060i	0.194447	−	0.00630362i
$939$	−0.849883	+	0.303689i	−0.0277349	+	0.00991050i
$940$	13.6822			0.446265
$941$	−15.5228	+	26.8862i	−0.506028	+	0.876466i	0.493948	+	0.869492i	$0.335553\pi$
$941$	−15.5228	+	26.8862i	−0.506028	+	0.876466i	−0.999976	+	0.00697439i	$0.997780\pi$
$942$	1.04115	−	5.70830i	0.0339225	−	0.185987i
$943$	−0.293537	−	0.508422i	−0.00955889	−	0.0165565i
$944$	−26.0809			−0.848863
$945$	−6.69717	+	12.0062i	−0.217859	+	0.390561i
$946$	−0.163049			−0.00530117
$947$	−7.94778	−	13.7660i	−0.258268	−	0.447334i	0.707510	−	0.706703i	$-0.249818\pi$
$947$	−7.94778	−	13.7660i	−0.258268	−	0.447334i	−0.965778	+	0.259370i	$0.916485\pi$
$948$	−3.08047	+	16.8893i	−0.100049	+	0.548539i
$949$	−8.70495	+	15.0774i	−0.282575	+	0.489433i
$950$	1.20789			0.0391891
$951$	30.7964	−	11.0045i	0.998640	−	0.356844i
$952$	5.85147	+	9.41661i	0.189647	+	0.305194i
$953$	−35.5025			−1.15004			−0.575019	−	0.818140i	$-0.695005\pi$
$953$	−35.5025			−1.15004			−0.575019	+	0.818140i	$0.695005\pi$
$954$	−6.61069	+	5.41592i	−0.214029	+	0.175347i
$955$	4.46643	+	7.73608i	0.144530	+	0.250334i
$956$	−48.6154			−1.57233
$957$	−29.4911	−	25.0428i	−0.953313	−	0.809518i
$958$	−2.37578	−	4.11498i	−0.0767581	−	0.132949i
$959$	−12.7773	+	0.414217i	−0.412601	+	0.0133758i
$960$	1.85041	−	10.1453i	0.0597218	−	0.327437i
$961$	−10.4259	−	18.0582i	−0.336319	−	0.582521i
$962$	5.01668	+	8.68915i	0.161744	+	0.280149i
$963$	−17.4356	+	14.2844i	−0.561855	+	0.460310i
$964$	−4.15717	+	7.20043i	−0.133893	+	0.231910i
$965$	0.852021	−	1.47574i	0.0274275	−	0.0475059i
$966$	1.24729	−	0.491825i	0.0401308	−	0.0158242i
$967$	−16.3359	−	28.2945i	−0.525326	−	0.909891i	−0.999565	−	0.0294948i	$-0.990610\pi$
$967$	−16.3359	−	28.2945i	−0.525326	−	0.909891i	0.474239	−	0.880396i	$-0.342723\pi$
$968$	−14.5535			−0.467769
$969$	−4.54494	+	24.9185i	−0.146005	+	0.800498i
$970$	4.07530			0.130850
$971$	−10.2895	+	17.8220i	−0.330207	+	0.571935i	−0.982552	−	0.185987i	$-0.940452\pi$
$971$	−10.2895	+	17.8220i	−0.330207	+	0.571935i	0.652345	+	0.757922i	$0.273785\pi$
$972$	−4.31003	−	29.4842i	−0.138244	−	0.945707i
$973$	−7.65456	−	12.3183i	−0.245394	−	0.394906i
$974$	−6.44968	+	11.1712i	−0.206661	+	0.357948i
$975$	−8.45740	+	3.02208i	−0.270854	+	0.0967841i
$976$	26.0624	−	45.1414i	0.834236	−	1.44494i
$977$	−5.11757	+	8.86390i	−0.163726	+	0.283581i	−0.936202	−	0.351462i	$-0.885685\pi$
$977$	−5.11757	+	8.86390i	−0.163726	+	0.283581i	0.772476	+	0.635044i	$0.219018\pi$
$978$	1.26346	−	6.92715i	0.0404009	−	0.221506i
$979$	−37.0458	+	64.1652i	−1.18399	+	2.05073i
$980$	−5.92573	+	11.9969i	−0.189290	+	0.383228i
$981$	−1.91837	−	11.6807i	−0.0612488	−	0.372936i
$982$	−0.652533	+	1.13022i	−0.0208232	+	0.0360668i
$983$	8.67049			0.276546			0.138273	−	0.990394i	$-0.455845\pi$
$983$	8.67049			0.276546			0.138273	+	0.990394i	$0.455845\pi$
$984$	1.13274	−	0.404760i	0.0361103	−	0.0129033i
$985$	16.0684			0.511982
$986$	−2.46772	−	4.27421i	−0.0785881	−	0.136119i
$987$	30.5145	−	12.0324i	0.971288	−	0.382994i
$988$	20.1240	−	34.8558i	0.640230	−	1.10891i
$989$	0.0555974	−	0.0962975i	0.00176789	−	0.00306208i
$990$	−0.701206	−	4.26955i	−0.0222858	−	0.135695i
$991$	26.8299	+	46.4708i	0.852280	+	1.47619i	0.879145	+	0.476554i	$0.158114\pi$
$991$	26.8299	+	46.4708i	0.852280	+	1.47619i	−0.0268650	+	0.999639i	$0.508552\pi$
$992$	12.1021	+	20.9614i	0.384241	+	0.665526i
$993$	−42.8617	+	15.3158i	−1.36018	+	0.486031i
$994$	4.23992	+	6.82318i	0.134482	+	0.216418i
$995$	4.15353	+	7.19412i	0.131676	+	0.228069i
$996$	34.0393	−	12.1633i	1.07858	−	0.385408i
$997$	14.8982			0.471830			0.235915	−	0.971774i	$-0.424191\pi$
$997$	14.8982			0.471830			0.235915	+	0.971774i	$0.424191\pi$
$998$	5.44267	+	9.42698i	0.172285	+	0.298406i
$999$	16.3818	+	29.5657i	0.518297	+	0.935418i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.k.b.16.6	✓	24
3.2	odd	2		945.2.k.b.856.7		24
7.4	even	3		315.2.l.b.151.7	yes	24
9.4	even	3		315.2.l.b.121.7	yes	24
9.5	odd	6		945.2.l.b.226.6		24
21.11	odd	6		945.2.l.b.46.6		24
63.4	even	3	inner	315.2.k.b.256.6	yes	24
63.32	odd	6		945.2.k.b.361.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.b.16.6	✓	24	1.1	even	1	trivial
315.2.k.b.256.6	yes	24	63.4	even	3	inner
315.2.l.b.121.7	yes	24	9.4	even	3
315.2.l.b.151.7	yes	24	7.4	even	3
945.2.k.b.361.7		24	63.32	odd	6
945.2.k.b.856.7		24	3.2	odd	2
945.2.l.b.46.6		24	21.11	odd	6
945.2.l.b.226.6		24	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.148731 - 0.257610i) q^{2} +(0.310785 - 1.70394i) q^{3} +(0.955758 - 1.65542i) q^{4} -1.00000 q^{5} +(-0.485175 + 0.173367i) q^{6} +(-2.64436 + 0.0857253i) q^{7} -1.16353 q^{8} +(-2.80683 - 1.05912i) q^{9} +O(q^{10})\)	\(q+(-0.148731 - 0.257610i) q^{2} +(0.310785 - 1.70394i) q^{3} +(0.955758 - 1.65542i) q^{4} -1.00000 q^{5} +(-0.485175 + 0.173367i) q^{6} +(-2.64436 + 0.0857253i) q^{7} -1.16353 q^{8} +(-2.80683 - 1.05912i) q^{9} +(0.148731 + 0.257610i) q^{10} +4.84852 q^{11} +(-2.52370 - 2.14304i) q^{12} +(-2.59263 - 4.49056i) q^{13} +(0.415382 + 0.668463i) q^{14} +(-0.310785 + 1.70394i) q^{15} +(-1.73846 - 3.01111i) q^{16} +(1.80070 + 3.11891i) q^{17} +(0.144623 + 0.880589i) q^{18} +(-2.03033 + 3.51663i) q^{19} +(-0.955758 + 1.65542i) q^{20} +(-0.675758 + 4.53248i) q^{21} +(-0.721125 - 1.24902i) q^{22} +0.983576 q^{23} +(-0.361607 + 1.98258i) q^{24} +1.00000 q^{25} +(-0.771208 + 1.33577i) q^{26} +(-2.67699 + 4.45350i) q^{27} +(-2.38546 + 4.45947i) q^{28} +(2.30352 - 3.98981i) q^{29} +(0.485175 - 0.173367i) q^{30} +(3.60041 - 6.23609i) q^{31} +(-1.68065 + 2.91098i) q^{32} +(1.50685 - 8.26159i) q^{33} +(0.535640 - 0.927756i) q^{34} +(2.64436 - 0.0857253i) q^{35} +(-4.43593 + 3.63422i) q^{36} +(3.25248 - 5.63347i) q^{37} +1.20789 q^{38} +(-8.45740 + 3.02208i) q^{39} +1.16353 q^{40} +(-0.298439 - 0.516911i) q^{41} +(1.26812 - 0.500038i) q^{42} +(0.0565258 - 0.0979056i) q^{43} +(4.63401 - 8.02634i) q^{44} +(2.80683 + 1.05912i) q^{45} +(-0.146288 - 0.253378i) q^{46} +(-3.57890 - 6.19883i) q^{47} +(-5.67104 + 2.02643i) q^{48} +(6.98530 - 0.453377i) q^{49} +(-0.148731 - 0.257610i) q^{50} +(5.87406 - 2.09898i) q^{51} -9.91170 q^{52} +(4.78827 + 8.29352i) q^{53} +(1.54542 + 0.0272455i) q^{54} -4.84852 q^{55} +(3.07679 - 0.0997437i) q^{56} +(5.36113 + 4.55247i) q^{57} -1.37042 q^{58} +(3.75057 - 6.49618i) q^{59} +(2.52370 + 2.14304i) q^{60} +(7.49581 + 12.9831i) q^{61} -2.14197 q^{62} +(7.51306 + 2.56008i) q^{63} -5.95400 q^{64} +(2.59263 + 4.49056i) q^{65} +(-2.35238 + 0.840575i) q^{66} +(3.78548 - 6.55664i) q^{67} +6.88414 q^{68} +(0.305681 - 1.67595i) q^{69} +(-0.415382 - 0.668463i) q^{70} +10.2073 q^{71} +(3.26582 + 1.23231i) q^{72} +(-1.67879 - 2.90775i) q^{73} -1.93498 q^{74} +(0.310785 - 1.70394i) q^{75} +(3.88100 + 6.72209i) q^{76} +(-12.8212 + 0.415641i) q^{77} +(2.03639 + 1.72923i) q^{78} +(-2.59268 - 4.49066i) q^{79} +(1.73846 + 3.01111i) q^{80} +(6.75654 + 5.94552i) q^{81} +(-0.0887742 + 0.153761i) q^{82} +(-5.45891 + 9.45512i) q^{83} +(6.85730 + 5.45062i) q^{84} +(-1.80070 - 3.11891i) q^{85} -0.0336285 q^{86} +(-6.08250 - 5.16504i) q^{87} -5.64138 q^{88} +(-7.64065 + 13.2340i) q^{89} +(-0.144623 - 0.880589i) q^{90} +(7.24080 + 11.6524i) q^{91} +(0.940061 - 1.62823i) q^{92} +(-9.50697 - 8.07296i) q^{93} +(-1.06458 + 1.84392i) q^{94} +(2.03033 - 3.51663i) q^{95} +(4.43781 + 3.76842i) q^{96} +(6.85013 - 11.8648i) q^{97} +(-1.15572 - 1.73205i) q^{98} +(-13.6089 - 5.13516i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9}+O(q^{10}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9	\( 24 q - q^{2} + q^{3} - 7 q^{4} - 24 q^{5} + 3 q^{6} + 7 q^{7} + 12 q^{8} + 9 q^{9} + q^{10} - 2 q^{11} - 16 q^{12} - 4 q^{13} - 13 q^{14} - q^{15} - 5 q^{16} - 7 q^{17} - 12 q^{18} - 2 q^{19} + 7 q^{20} - 5 q^{21} + 19 q^{22} - 2 q^{23} - 30 q^{24} + 24 q^{25} + 11 q^{26} - 11 q^{27} - 28 q^{28} - 3 q^{30} + 8 q^{31} + 17 q^{32} + q^{33} + q^{34} - 7 q^{35} - 25 q^{36} + 17 q^{37} + 70 q^{38} - 8 q^{39} - 12 q^{40} + 20 q^{41} - 15 q^{42} + 31 q^{43} - 7 q^{44} - 9 q^{45} - 10 q^{46} - 31 q^{47} - 36 q^{48} - 11 q^{49} - q^{50} - 37 q^{51} + 8 q^{52} + 8 q^{53} + 111 q^{54} + 2 q^{55} + 45 q^{56} + 5 q^{57} - 90 q^{58} - 21 q^{59} + 16 q^{60} + 5 q^{61} + 14 q^{62} - 9 q^{63} - 56 q^{64} + 4 q^{65} + 46 q^{66} + 43 q^{67} + 96 q^{68} + 26 q^{69} + 13 q^{70} + 24 q^{71} - 69 q^{72} - 18 q^{73} - 18 q^{74} + q^{75} - 13 q^{76} + 5 q^{77} + 19 q^{78} + 40 q^{79} + 5 q^{80} - 39 q^{81} + 5 q^{82} - 60 q^{83} + 47 q^{84} + 7 q^{85} - 24 q^{86} - 61 q^{87} - 100 q^{88} - 4 q^{89} + 12 q^{90} - 33 q^{91} - 18 q^{92} - 8 q^{93} - 11 q^{94} + 2 q^{95} + 6 q^{96} + 6 q^{97} - 15 q^{98} - q^{99}+O(q^{100}) \) 24 * q - q^2 + q^3 - 7 * q^4 - 24 * q^5 + 3 * q^6 + 7 * q^7 + 12 * q^8 + 9 * q^9 + q^10 - 2 * q^11 - 16 * q^12 - 4 * q^13 - 13 * q^14 - q^15 - 5 * q^16 - 7 * q^17 - 12 * q^18 - 2 * q^19 + 7 * q^20 - 5 * q^21 + 19 * q^22 - 2 * q^23 - 30 * q^24 + 24 * q^25 + 11 * q^26 - 11 * q^27 - 28 * q^28 - 3 * q^30 + 8 * q^31 + 17 * q^32 + q^33 + q^34 - 7 * q^35 - 25 * q^36 + 17 * q^37 + 70 * q^38 - 8 * q^39 - 12 * q^40 + 20 * q^41 - 15 * q^42 + 31 * q^43 - 7 * q^44 - 9 * q^45 - 10 * q^46 - 31 * q^47 - 36 * q^48 - 11 * q^49 - q^50 - 37 * q^51 + 8 * q^52 + 8 * q^53 + 111 * q^54 + 2 * q^55 + 45 * q^56 + 5 * q^57 - 90 * q^58 - 21 * q^59 + 16 * q^60 + 5 * q^61 + 14 * q^62 - 9 * q^63 - 56 * q^64 + 4 * q^65 + 46 * q^66 + 43 * q^67 + 96 * q^68 + 26 * q^69 + 13 * q^70 + 24 * q^71 - 69 * q^72 - 18 * q^73 - 18 * q^74 + q^75 - 13 * q^76 + 5 * q^77 + 19 * q^78 + 40 * q^79 + 5 * q^80 - 39 * q^81 + 5 * q^82 - 60 * q^83 + 47 * q^84 + 7 * q^85 - 24 * q^86 - 61 * q^87 - 100 * q^88 - 4 * q^89 + 12 * q^90 - 33 * q^91 - 18 * q^92 - 8 * q^93 - 11 * q^94 + 2 * q^95 + 6 * q^96 + 6 * q^97 - 15 * q^98 - q^99

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